In seven-dimensional geometry, a 7-polytope is a polytope contained by 6-polytope facets. Each 5-polytope ridge being shared by exactly two 6-polytope facets.

A uniform 7-polytope is one whose symmetry group is transitive on vertices and whose facets are uniform 6-polytopes.

Regular 7-polytopes

Regular 7-polytopes are represented by the Schläfli symbol {p,q,r,s,t,u} with u {p,q,r,s,t} 6-polytopes facets around each 4-face.

There are exactly three such convex regular 7-polytopes:

{3,3,3,3,3,3} - 7-simplex
{4,3,3,3,3,3} - 7-cube
{3,3,3,3,3,4} - 7-orthoplex

There are no nonconvex regular 7-polytopes.

Characteristics

The topology of any given 7-polytope is defined by its Betti numbers and torsion coefficients.Richeson, D.; Euler's Gem: The Polyhedron Formula and the Birth of Topoplogy, Princeton, 2008.

The value of the Euler characteristic used to characterise polyhedra does not generalize usefully to higher dimensions, whatever their underlying topology. This inadequacy of the Euler characteristic to reliably distinguish between different topologies in higher dimensions led to the discovery of the more sophisticated Betti numbers.

Similarly, the notion of orientability of a polyhedron is insufficient to characterise the surface twistings of toroidal polytopes, and this led to the use of torsion coefficients.

Uniform 7-polytopes by fundamental Coxeter groups

Uniform 7-polytopes with reflective symmetry can be generated by these four Coxeter groups, represented by permutations of rings of the Coxeter-Dynkin diagrams:

# !colspan=3\|Coxeter group !Regular and semiregular forms !Uniform count
class="wikitable"
1	A₇	[3⁶]	{{CDD\|node\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node}} \| 7-simplex - {3⁶}, {{CDD\|node_1\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node}} \|71
2	B₇	[4,3⁵]	{{CDD\|node\|4\|node\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node}} \| 7-cube - {4,3⁵}, {{CDD\|node_1\|4\|node\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node}} 7-orthoplex - {3⁵,4}, {{CDD\|node_1\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node\|4\|node}} 7-demicube - h{4,3⁵}, {{CDD\|node_h\|4\|node\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node}} \|127 + 32
3	D₇	[3^3,1,1]	{{CDD\|nodes\|split2\|node\|3\|node\|3\|node\|3\|node\|3\|node}} \| 7-demicube, {3,3^4,1}, {{CDD\|nodes_10ru\|split2\|node\|3\|node\|3\|node\|3\|node\|3\|node}} 7-orthoplex, {3⁴,3^1,1}, {{CDD\|node_1\|3\|node\|3\|node\|3\|node\|3\|node\|split1\|nodes}} \|95 (0 unique)
4	E₇	[3^3,2,1]	{{CDD\|nodea\|3a\|nodea\|3a\|branch\|3a\|nodea\|3a\|nodea\|3a\|nodea}} \| 3₂₁ - {{CDD\|nodea\|3a\|nodea\|3a\|branch\|3a\|nodea\|3a\|nodea\|3a\|nodea_1}} 1₃₂ - {{CDD\|nodea\|3a\|nodea\|3a\|branch_01lr\|3a\|nodea\|3a\|nodea\|3a\|nodea}} 2₃₁ - {{CDD\|nodea_1\|3a\|nodea\|3a\|branch\|3a\|nodea\|3a\|nodea\|3a\|nodea}} \|127

# !colspan=2\|Coxeter group !Coxeter diagram
class="wikitable collapsed collapsible" !colspan=12\|Prismatic finite Coxeter groups
colspan=4\|6+1
1	A₆A₁	[3⁵]×[ ]	{{CDD\|node\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node\|2\|node}}
2	BC₆A₁	[4,3⁴]×[ ]	{{CDD\|node\|4\|node\|3\|node\|3\|node\|3\|node\|3\|node\|2\|node}}
3	D₆A₁	[3^3,1,1]×[ ]	{{CDD\|nodes\|split2\|node\|3\|node\|3\|node\|3\|node\|2\|node}}
4	E₆A₁	[3^2,2,1]×[ ]	{{CDD\|nodea\|3a\|nodea\|3a\|branch\|3a\|nodea\|3a\|nodea\|2\|nodea}}
colspan=4\|5+2
1	A₅I₂(p)	[3,3,3]×[p]	{{CDD\|node\|3\|node\|3\|node\|3\|node\|3\|node\|2\|node\|p\|node}}
2	BC₅I₂(p)	[4,3,3]×[p]	{{CDD\|node\|4\|node\|3\|node\|3\|node\|3\|node\|2\|node\|p\|node}}
3	D₅I₂(p)	[3^2,1,1]×[p]	{{CDD\|nodes\|split2\|node\|3\|node\|3\|node\|2\|node\|p\|node}}
colspan=4\|5+1+1
1	A₅A₁²	[3,3,3]×[ ]²	{{CDD\|node\|3\|node\|3\|node\|3\|node\|3\|node\|2\|node\|2\|node}}
2	BC₅A₁²	[4,3,3]×[ ]²	{{CDD\|node\|4\|node\|3\|node\|3\|node\|3\|node\|2\|node\|2\|node}}
3	D₅A₁²	[3^2,1,1]×[ ]²	{{CDD\|nodes\|split2\|node\|3\|node\|3\|node\|2\|node\|2\|node}}
colspan=4\|4+3
1	A₄A₃	[3,3,3]×[3,3]	{{CDD\|node\|3\|node\|3\|node\|3\|node\|2\|node\|3\|node\|3\|node}}
2	A₄B₃	[3,3,3]×[4,3]	{{CDD\|node\|3\|node\|3\|node\|3\|node\|2\|node\|4\|node\|3\|node}}
3	A₄H₃	[3,3,3]×[5,3]	{{CDD\|node\|3\|node\|3\|node\|3\|node\|2\|node\|5\|node\|3\|node}}
4	BC₄A₃	[4,3,3]×[3,3]	{{CDD\|node\|4\|node\|3\|node\|3\|node\|2\|node\|3\|node\|3\|node}}
5	BC₄B₃	[4,3,3]×[4,3]	{{CDD\|node\|4\|node\|3\|node\|3\|node\|2\|node\|4\|node\|3\|node}}
6	BC₄H₃	[4,3,3]×[5,3]	{{CDD\|node\|4\|node\|3\|node\|3\|node\|2\|node\|5\|node\|3\|node}}
7	H₄A₃	[5,3,3]×[3,3]	{{CDD\|node\|5\|node\|3\|node\|3\|node\|2\|node\|3\|node\|3\|node}}
8	H₄B₃	[5,3,3]×[4,3]	{{CDD\|node\|5\|node\|3\|node\|3\|node\|2\|node\|4\|node\|3\|node}}
9	H₄H₃	[5,3,3]×[5,3]	{{CDD\|node\|5\|node\|3\|node\|3\|node\|2\|node\|5\|node\|3\|node}}
10	F₄A₃	[3,4,3]×[3,3]	{{CDD\|node\|3\|node\|4\|node\|3\|node\|2\|node\|3\|node\|3\|node}}
11	F₄B₃	[3,4,3]×[4,3]	{{CDD\|node\|3\|node\|4\|node\|3\|node\|2\|node\|4\|node\|3\|node}}
12	F₄H₃	[3,4,3]×[5,3]	{{CDD\|node\|3\|node\|4\|node\|3\|node\|2\|node\|5\|node\|3\|node}}
13	D₄A₃	[3^1,1,1]×[3,3]	{{CDD\|nodes\|split2\|node\|3\|node\|2\|node\|3\|node\|3\|node}}
14	D₄B₃	[3^1,1,1]×[4,3]	{{CDD\|nodes\|split2\|node\|3\|node\|2\|node\|4\|node\|3\|node}}
15	D₄H₃	[3^1,1,1]×[5,3]	{{CDD\|nodes\|split2\|node\|3\|node\|2\|node\|5\|node\|3\|node}}
colspan=4\|4+2+1
1	A₄I₂(p)A₁	[3,3,3]×[p]×[ ]	{{CDD\|node\|3\|node\|3\|node\|3\|node\|2\|node\|p\|node\|2\|node}}
2	BC₄I₂(p)A₁	[4,3,3]×[p]×[ ]	{{CDD\|node\|4\|node\|3\|node\|3\|node\|2\|node\|p\|node\|2\|node}}
3	F₄I₂(p)A₁	[3,4,3]×[p]×[ ]	{{CDD\|node\|3\|node\|4\|node\|3\|node\|2\|node\|p\|node\|2\|node}}
4	H₄I₂(p)A₁	[5,3,3]×[p]×[ ]	{{CDD\|node\|5\|node\|3\|node\|3\|node\|2\|node\|p\|node\|2\|node}}
5	D₄I₂(p)A₁	[3^1,1,1]×[p]×[ ]	{{CDD\|nodes\|split2\|node\|3\|node\|2\|node\|p\|node\|2\|node}}
colspan=4\|4+1+1+1
1	A₄A₁³	[3,3,3]×[ ]³	{{CDD\|node\|3\|node\|3\|node\|3\|node\|2\|node\|2\|node\|2\|node}}
2	BC₄A₁³	[4,3,3]×[ ]³	{{CDD\|node\|4\|node\|3\|node\|3\|node\|2\|node\|2\|node\|2\|node}}
3	F₄A₁³	[3,4,3]×[ ]³	{{CDD\|node\|3\|node\|4\|node\|3\|node\|2\|node\|2\|node\|2\|node}}
4	H₄A₁³	[5,3,3]×[ ]³	{{CDD\|node\|5\|node\|3\|node\|3\|node\|2\|node\|2\|node\|2\|node}}
5	D₄A₁³	[3^1,1,1]×[ ]³	{{CDD\|nodes\|split2\|node\|3\|node\|2\|node\|2\|node\|2\|node}}
colspan=4\|3+3+1
1	A₃A₃A₁	[3,3]×[3,3]×[ ]	{{CDD\|node\|3\|node\|3\|node\|2\|node\|3\|node\|3\|node\|2\|node}}
2	A₃B₃A₁	[3,3]×[4,3]×[ ]	{{CDD\|node\|3\|node\|3\|node\|2\|node\|4\|node\|3\|node\|2\|node}}
3	A₃H₃A₁	[3,3]×[5,3]×[ ]	{{CDD\|node\|3\|node\|3\|node\|2\|node\|5\|node\|3\|node\|2\|node}}
4	BC₃B₃A₁	[4,3]×[4,3]×[ ]	{{CDD\|node\|4\|node\|3\|node\|2\|node\|4\|node\|3\|node\|2\|node}}
5	BC₃H₃A₁	[4,3]×[5,3]×[ ]	{{CDD\|node\|4\|node\|3\|node\|2\|node\|5\|node\|3\|node\|2\|node}}
6	H₃A₃A₁	[5,3]×[5,3]×[ ]	{{CDD\|node\|5\|node\|3\|node\|2\|node\|5\|node\|3\|node\|2\|node}}
colspan=4\|3+2+2
1	A₃I₂(p)I₂(q)	[3,3]×[p]×[q]	{{CDD\|node\|3\|node\|3\|node\|2\|node\|p\|node\|2\|node\|q\|node}}
2	BC₃I₂(p)I₂(q)	[4,3]×[p]×[q]	{{CDD\|node\|4\|node\|3\|node\|2\|node\|p\|node\|2\|node\|q\|node}}
3	H₃I₂(p)I₂(q)	[5,3]×[p]×[q]	{{CDD\|node\|5\|node\|3\|node\|2\|node\|p\|node\|2\|node\|q\|node}}
colspan=4\|3+2+1+1
1	A₃I₂(p)A₁²	[3,3]×[p]×[ ]²	{{CDD\|node\|3\|node\|3\|node\|2\|node\|p\|node\|2\|node\|2\|node}}
2	BC₃I₂(p)A₁²	[4,3]×[p]×[ ]²	{{CDD\|node\|4\|node\|3\|node\|2\|node\|p\|node\|2\|node\|2\|node}}
3	H₃I₂(p)A₁²	[5,3]×[p]×[ ]²	{{CDD\|node\|5\|node\|3\|node\|2\|node\|p\|node\|2\|node\|2\|node}}
colspan=4\|3+1+1+1+1
1	A₃A₁⁴	[3,3]×[ ]⁴	{{CDD\|node\|3\|node\|3\|node\|2\|node\|2\|node\|2\|node\|2\|node}}
2	BC₃A₁⁴	[4,3]×[ ]⁴	{{CDD\|node\|4\|node\|3\|node\|2\|node\|2\|node\|2\|node\|2\|node}}
3	H₃A₁⁴	[5,3]×[ ]⁴	{{CDD\|node\|5\|node\|3\|node\|2\|node\|2\|node\|2\|node\|2\|node}}
colspan=4\|2+2+2+1
1	I₂(p)I₂(q)I₂(r)A₁	[p]×[q]×[r]×[ ]	{{CDD\|node\|p\|node\|2\|node\|q\|node\|2\|node\|r\|node\|2\|node}}
colspan=4\|2+2+1+1+1
1	I₂(p)I₂(q)A₁³	[p]×[q]×[ ]³	{{CDD\|node\|p\|node\|2\|node\|q\|node\|2\|node\|2\|node\|2\|node}}
colspan=4\|2+1+1+1+1+1
1	I₂(p)A₁⁵	[p]×[ ]⁵	{{CDD\|node\|p\|node\|2\|node\|2\|node\|2\|node\|2\|node\|2\|node}}
colspan=4\|1+1+1+1+1+1+1
1	A₁⁷	[ ]⁷	{{CDD\|node\|2\|node\|2\|node\|2\|node\|2\|node\|2\|node\|2\|node}}

The A7 family

The A₇ family has symmetry of order 40320 (8 factorial).

There are 71 (64+8-1) forms based on all permutations of the Coxeter-Dynkin diagrams with one or more rings. All 71 are enumerated below. Norman Johnson's truncation names are given. Bowers names and acronym are also given for cross-referencing.

See also a list of A7 polytopes for symmetric Coxeter plane graphs of these polytopes.

rowspan=2\|# !rowspan=2\|Coxeter-Dynkin diagram !rowspan=2\|Truncation indices !rowspan=2\|Johnson name Bowers name (and acronym) !rowspan=2\|Basepoint !colspan=7\|Element counts
class="wikitable collapsible collapsed" !colspan=12\|A₇ uniform polytopes
6\|\| 5\|\| 4\|\| 3\|\| 2\|\| 1\|\| 0
style="text-align:center;" \|1	{{CDD\|node\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node_1}}	t₀	7-simplex (oca)	(0,0,0,0,0,0,0,1)	8	28	56	70	56	28	8
style="text-align:center;" \|2	{{CDD\|node\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node_1\|3\|node}}	t₁	Rectified 7-simplex (roc)	(0,0,0,0,0,0,1,1)	16	84	224	350	336	168	28
style="text-align:center;" \|3	{{CDD\|node\|3\|node\|3\|node\|3\|node\|3\|node_1\|3\|node\|3\|node}}	t₂	Birectified 7-simplex (broc)	(0,0,0,0,0,1,1,1)	16	112	392	770	840	420	56
style="text-align:center; background:#e0f0e0;" \|4	{{CDD\|node\|3\|node\|3\|node\|3\|node_1\|3\|node\|3\|node\|3\|node}}	t₃	Trirectified 7-simplex (he)	(0,0,0,0,1,1,1,1)	16	112	448	980	1120	560	70
style="text-align:center;" \|5	{{CDD\|node\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node_1\|3\|node_1}}	t_0,1	Truncated 7-simplex (toc)	(0,0,0,0,0,0,1,2)	16	84	224	350	336	196	56
style="text-align:center;" \|6	{{CDD\|node\|3\|node\|3\|node\|3\|node\|3\|node_1\|3\|node\|3\|node_1}}	t_0,2	Cantellated 7-simplex (saro)	(0,0,0,0,0,1,1,2)	44	308	980	1750	1876	1008	168
style="text-align:center;" \|7	{{CDD\|node\|3\|node\|3\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node}}	t_1,2	Bitruncated 7-simplex (bittoc)	(0,0,0,0,0,1,2,2)						588	168
style="text-align:center;" \|8	{{CDD\|node\|3\|node\|3\|node\|3\|node_1\|3\|node\|3\|node\|3\|node_1}}	t_0,3	Runcinated 7-simplex (spo)	(0,0,0,0,1,1,1,2)	100	756	2548	4830	4760	2100	280
style="text-align:center;" \|9	{{CDD\|node\|3\|node\|3\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node}}	t_1,3	Bicantellated 7-simplex (sabro)	(0,0,0,0,1,1,2,2)						2520	420
style="text-align:center;" \|10	{{CDD\|node\|3\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node}}	t_2,3	Tritruncated 7-simplex (tattoc)	(0,0,0,0,1,2,2,2)						980	280
style="text-align:center;" \|11	{{CDD\|node\|3\|node\|3\|node_1\|3\|node\|3\|node\|3\|node\|3\|node_1}}	t_0,4	Stericated 7-simplex (sco)	(0,0,0,1,1,1,1,2)						2240	280
style="text-align:center;" \|12	{{CDD\|node\|3\|node\|3\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node}}	t_1,4	Biruncinated 7-simplex (sibpo)	(0,0,0,1,1,1,2,2)						4200	560
style="text-align:center; background:#e0f0e0;" \|13	{{CDD\|node\|3\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node}}	t_2,4	Tricantellated 7-simplex (stiroh)	(0,0,0,1,1,2,2,2)						3360	560
style="text-align:center;" \|14	{{CDD\|node\|3\|node_1\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node_1}}	t_0,5	Pentellated 7-simplex (seto)	(0,0,1,1,1,1,1,2)						1260	168
style="text-align:center; background:#e0f0e0;" \|15	{{CDD\|node\|3\|node_1\|3\|node\|3\|node\|3\|node\|3\|node_1\|3\|node}}	t_1,5	Bistericated 7-simplex (sabach)	(0,0,1,1,1,1,2,2)						3360	420
style="text-align:center; background:#e0f0e0;" \|16	{{CDD\|node_1\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node_1}}	t_0,6	Hexicated 7-simplex (suph)	(0,1,1,1,1,1,1,2)						336	56
style="text-align:center;" \|17	{{CDD\|node\|3\|node\|3\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1}}	t_0,1,2	Cantitruncated 7-simplex (garo)	(0,0,0,0,0,1,2,3)						1176	336
style="text-align:center;" \|18	{{CDD\|node\|3\|node\|3\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1}}	t_0,1,3	Runcitruncated 7-simplex (patto)	(0,0,0,0,1,1,2,3)						4620	840
style="text-align:center;" \|19	{{CDD\|node\|3\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1}}	t_0,2,3	Runcicantellated 7-simplex (paro)	(0,0,0,0,1,2,2,3)						3360	840
style="text-align:center;" \|20	{{CDD\|node\|3\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node}}	t_1,2,3	Bicantitruncated 7-simplex (gabro)	(0,0,0,0,1,2,3,3)						2940	840
style="text-align:center;" \|21	{{CDD\|node\|3\|node\|3\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node_1}}	t_0,1,4	Steritruncated 7-simplex (cato)	(0,0,0,1,1,1,2,3)						7280	1120
style="text-align:center;" \|22	{{CDD\|node\|3\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node_1}}	t_0,2,4	Stericantellated 7-simplex (caro)	(0,0,0,1,1,2,2,3)						10080	1680
style="text-align:center;" \|23	{{CDD\|node\|3\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node}}	t_1,2,4	Biruncitruncated 7-simplex (bipto)	(0,0,0,1,1,2,3,3)						8400	1680
style="text-align:center;" \|24	{{CDD\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node\|3\|node_1}}	t_0,3,4	Steriruncinated 7-simplex (cepo)	(0,0,0,1,2,2,2,3)						5040	1120
style="text-align:center;" \|25	{{CDD\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node}}	t_1,3,4	Biruncicantellated 7-simplex (bipro)	(0,0,0,1,2,2,3,3)						7560	1680
style="text-align:center; background:#e0f0e0;" \|26	{{CDD\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node}}	t_2,3,4	Tricantitruncated 7-simplex (gatroh)	(0,0,0,1,2,3,3,3)						3920	1120
style="text-align:center;" \|27	{{CDD\|node\|3\|node_1\|3\|node\|3\|node\|3\|node\|3\|node_1\|3\|node_1}}	t_0,1,5	Pentitruncated 7-simplex (teto)	(0,0,1,1,1,1,2,3)						5460	840
style="text-align:center;" \|28	{{CDD\|node\|3\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node\|3\|node_1}}	t_0,2,5	Penticantellated 7-simplex (tero)	(0,0,1,1,1,2,2,3)						11760	1680
style="text-align:center;" \|29	{{CDD\|node\|3\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node}}	t_1,2,5	Bisteritruncated 7-simplex (bacto)	(0,0,1,1,1,2,3,3)						9240	1680
style="text-align:center;" \|30	{{CDD\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node\|3\|node_1}}	t_0,3,5	Pentiruncinated 7-simplex (tepo)	(0,0,1,1,2,2,2,3)						10920	1680
style="text-align:center; background:#e0f0e0;" \|31	{{CDD\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node}}	t_1,3,5	Bistericantellated 7-simplex (bacroh)	(0,0,1,1,2,2,3,3)						15120	2520
style="text-align:center;" \|32	{{CDD\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node\|3\|node\|3\|node_1}}	t_0,4,5	Pentistericated 7-simplex (teco)	(0,0,1,2,2,2,2,3)						4200	840
style="text-align:center;" \|33	{{CDD\|node_1\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node_1\|3\|node_1}}	t_0,1,6	Hexitruncated 7-simplex (puto)	(0,1,1,1,1,1,2,3)						1848	336
style="text-align:center;" \|34	{{CDD\|node_1\|3\|node\|3\|node\|3\|node\|3\|node_1\|3\|node\|3\|node_1}}	t_0,2,6	Hexicantellated 7-simplex (puro)	(0,1,1,1,1,2,2,3)						5880	840
style="text-align:center; background:#e0f0e0;" \|35	{{CDD\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node\|3\|node\|3\|node_1}}	t_0,3,6	Hexiruncinated 7-simplex (puph)	(0,1,1,1,2,2,2,3)						8400	1120
style="text-align:center;" \|36	{{CDD\|node\|3\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1}}	t_0,1,2,3	Runcicantitruncated 7-simplex (gapo)	(0,0,0,0,1,2,3,4)						5880	1680
style="text-align:center;" \|37	{{CDD\|node\|3\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1}}	t_0,1,2,4	Stericantitruncated 7-simplex (cagro)	(0,0,0,1,1,2,3,4)						16800	3360
style="text-align:center;" \|38	{{CDD\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1}}	t_0,1,3,4	Steriruncitruncated 7-simplex (capto)	(0,0,0,1,2,2,3,4)						13440	3360
style="text-align:center;" \|39	{{CDD\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1}}	t_0,2,3,4	Steriruncicantellated 7-simplex (capro)	(0,0,0,1,2,3,3,4)						13440	3360
style="text-align:center;" \|40	{{CDD\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node}}	t_1,2,3,4	Biruncicantitruncated 7-simplex (gibpo)	(0,0,0,1,2,3,4,4)						11760	3360
style="text-align:center;" \|41	{{CDD\|node\|3\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1}}	t_0,1,2,5	Penticantitruncated 7-simplex (tegro)	(0,0,1,1,1,2,3,4)						18480	3360
style="text-align:center;" \|42	{{CDD\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1}}	t_0,1,3,5	Pentiruncitruncated 7-simplex (tapto)	(0,0,1,1,2,2,3,4)						27720	5040
style="text-align:center;" \|43	{{CDD\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1}}	t_0,2,3,5	Pentiruncicantellated 7-simplex (tapro)	(0,0,1,1,2,3,3,4)						25200	5040
style="text-align:center;" \|44	{{CDD\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node}}	t_1,2,3,5	Bistericantitruncated 7-simplex (bacogro)	(0,0,1,1,2,3,4,4)						22680	5040
style="text-align:center;" \|45	{{CDD\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node_1}}	t_0,1,4,5	Pentisteritruncated 7-simplex (tecto)	(0,0,1,2,2,2,3,4)						15120	3360
style="text-align:center;" \|46	{{CDD\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node_1}}	t_0,2,4,5	Pentistericantellated 7-simplex (tecro)	(0,0,1,2,2,3,3,4)						25200	5040
style="text-align:center; background:#e0f0e0;" \|47	{{CDD\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node}}	t_1,2,4,5	Bisteriruncitruncated 7-simplex (bicpath)	(0,0,1,2,2,3,4,4)						20160	5040
style="text-align:center;" \|48	{{CDD\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node\|3\|node_1}}	t_0,3,4,5	Pentisteriruncinated 7-simplex (tacpo)	(0,0,1,2,3,3,3,4)						15120	3360
style="text-align:center;" \|49	{{CDD\|node_1\|3\|node\|3\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1}}	t_0,1,2,6	Hexicantitruncated 7-simplex (pugro)	(0,1,1,1,1,2,3,4)						8400	1680
style="text-align:center;" \|50	{{CDD\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1}}	t_0,1,3,6	Hexiruncitruncated 7-simplex (pugato)	(0,1,1,1,2,2,3,4)						20160	3360
style="text-align:center;" \|51	{{CDD\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1}}	t_0,2,3,6	Hexiruncicantellated 7-simplex (pugro)	(0,1,1,1,2,3,3,4)						16800	3360
style="text-align:center;" \|52	{{CDD\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node_1}}	t_0,1,4,6	Hexisteritruncated 7-simplex (pucto)	(0,1,1,2,2,2,3,4)						20160	3360
style="text-align:center; background:#e0f0e0;" \|53	{{CDD\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node_1}}	t_0,2,4,6	Hexistericantellated 7-simplex (pucroh)	(0,1,1,2,2,3,3,4)						30240	5040
style="text-align:center; background:#e0f0e0;" \|54	{{CDD\|node_1\|3\|node_1\|3\|node\|3\|node\|3\|node\|3\|node_1\|3\|node_1}}	t_0,1,5,6	Hexipentitruncated 7-simplex (putath)	(0,1,2,2,2,2,3,4)						8400	1680
style="text-align:center;" \|55	{{CDD\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1}}	t_0,1,2,3,4	Steriruncicantitruncated 7-simplex (gecco)	(0,0,0,1,2,3,4,5)						23520	6720
style="text-align:center;" \|56	{{CDD\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1}}	t_0,1,2,3,5	Pentiruncicantitruncated 7-simplex (tegapo)	(0,0,1,1,2,3,4,5)						45360	10080
style="text-align:center;" \|57	{{CDD\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1}}	t_0,1,2,4,5	Pentistericantitruncated 7-simplex (tecagro)	(0,0,1,2,2,3,4,5)						40320	10080
style="text-align:center;" \|58	{{CDD\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1}}	t_0,1,3,4,5	Pentisteriruncitruncated 7-simplex (tacpeto)	(0,0,1,2,3,3,4,5)						40320	10080
style="text-align:center;" \|59	{{CDD\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1}}	t_0,2,3,4,5	Pentisteriruncicantellated 7-simplex (tacpro)	(0,0,1,2,3,4,4,5)						40320	10080
style="text-align:center; background:#e0f0e0;" \|60	{{CDD\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node}}	t_1,2,3,4,5	Bisteriruncicantitruncated 7-simplex (gabach)	(0,0,1,2,3,4,5,5)						35280	10080
style="text-align:center;" \|61	{{CDD\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1}}	t_0,1,2,3,6	Hexiruncicantitruncated 7-simplex (pugopo)	(0,1,1,1,2,3,4,5)						30240	6720
style="text-align:center;" \|62	{{CDD\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1}}	t_0,1,2,4,6	Hexistericantitruncated 7-simplex (pucagro)	(0,1,1,2,2,3,4,5)						50400	10080
style="text-align:center;" \|63	{{CDD\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1}}	t_0,1,3,4,6	Hexisteriruncitruncated 7-simplex (pucpato)	(0,1,1,2,3,3,4,5)						45360	10080
style="text-align:center; background:#e0f0e0;" \|64	{{CDD\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1}}	t_0,2,3,4,6	Hexisteriruncicantellated 7-simplex (pucproh)	(0,1,1,2,3,4,4,5)						45360	10080
style="text-align:center;" \|65	{{CDD\|node_1\|3\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1}}	t_0,1,2,5,6	Hexipenticantitruncated 7-simplex (putagro)	(0,1,2,2,2,3,4,5)						30240	6720
style="text-align:center; background:#e0f0e0;" \|66	{{CDD\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1}}	t_0,1,3,5,6	Hexipentiruncitruncated 7-simplex (putpath)	(0,1,2,2,3,3,4,5)						50400	10080
style="text-align:center;" \|67	{{CDD\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1}}	t_0,1,2,3,4,5	Pentisteriruncicantitruncated 7-simplex (geto)	(0,0,1,2,3,4,5,6)						70560	20160
style="text-align:center;" \|68	{{CDD\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1}}	t_0,1,2,3,4,6	Hexisteriruncicantitruncated 7-simplex (pugaco)	(0,1,1,2,3,4,5,6)						80640	20160
style="text-align:center;" \|69	{{CDD\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1}}	t_0,1,2,3,5,6	Hexipentiruncicantitruncated 7-simplex (putgapo)	(0,1,2,2,3,4,5,6)						80640	20160
style="text-align:center; background:#e0f0e0;" \|70	{{CDD\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1}}	t_0,1,2,4,5,6	Hexipentistericantitruncated 7-simplex (putcagroh)	(0,1,2,3,3,4,5,6)						80640	20160
style="text-align:center; background:#e0f0e0;" \|71	{{CDD\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1}}	t_{0,1,2,3,4,5,6}	Omnitruncated 7-simplex (guph)	(0,1,2,3,4,5,6,7)						141120	40320

The B7 family

The B₇ family has symmetry of order 645120 (7 factorial x 2⁷).

There are 127 forms based on all permutations of the Coxeter-Dynkin diagrams with one or more rings. Johnson and Bowers names.

See also a list of B7 polytopes for symmetric Coxeter plane graphs of these polytopes.

rowspan=2\|# !rowspan=2\|Coxeter-Dynkin diagram t-notation !rowspan=2\|Name (BSA) !rowspan=2\|Base point !colspan=7\|Element counts
class="wikitable collapsible collapsed !colspan=12\|B₇ uniform polytopes
6\|\|5\|\|4\|\|3\|\|2\|\|1\|\|0
style="text-align:center; background:#f0e0e0;" !1 \|{{CDD\|node\|4\|node\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node_1}} t₀{3,3,3,3,3,4}	7-orthoplex (zee)	\|(0,0,0,0,0,0,1)√2	128	448	672	560	280	84	14
style="text-align:center; background:#f0e0e0;" !2 \|{{CDD\|node\|4\|node\|3\|node\|3\|node\|3\|node\|3\|node_1\|3\|node}} t₁{3,3,3,3,3,4}	Rectified 7-orthoplex (rez)	\|(0,0,0,0,0,1,1)√2	142	1344	3360	3920	2520	840	84
style="text-align:center; background:#f0e0e0;" !3 \|{{CDD\|node\|4\|node\|3\|node\|3\|node\|3\|node_1\|3\|node\|3\|node}} t₂{3,3,3,3,3,4}	Birectified 7-orthoplex (barz)	\|(0,0,0,0,1,1,1)√2	142	1428	6048	10640	8960	3360	280
style="text-align:center; background:#e0f0e0;" !4 \|{{CDD\|node\|4\|node\|3\|node\|3\|node_1\|3\|node\|3\|node\|3\|node}} t₃{4,3,3,3,3,3}	Trirectified 7-cube (sez)	\|(0,0,0,1,1,1,1)√2	142	1428	6328	14560	15680	6720	560
style="text-align:center; background:#e0e0f0;" !5 \|{{CDD\|node\|4\|node\|3\|node_1\|3\|node\|3\|node\|3\|node\|3\|node}} t₂{4,3,3,3,3,3}	Birectified 7-cube (bersa)	\|(0,0,1,1,1,1,1)√2	142	1428	5656	11760	13440	6720	672
style="text-align:center; background:#e0e0f0;" !6 \|{{CDD\|node\|4\|node_1\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node}} t₁{4,3,3,3,3,3}	Rectified 7-cube (rasa)	\|(0,1,1,1,1,1,1)√2	142	980	2968	5040	5152	2688	448
style="text-align:center; background:#e0e0f0;" !7 \|{{CDD\|node_1\|4\|node\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node}} t₀{4,3,3,3,3,3}	7-cube (hept)	\|(0,0,0,0,0,0,0)√2 + (1,1,1,1,1,1,1)	14	84	280	560	672	448	128
style="text-align:center; background:#f0e0e0;" !8 \|{{CDD\|node\|4\|node\|3\|node\|3\|node\|3\|node\|3\|node_1\|3\|node_1}} t_0,1{3,3,3,3,3,4}	Truncated 7-orthoplex (Taz)	\|(0,0,0,0,0,1,2)√2	142	1344	3360	4760	2520	924	168
style="text-align:center; background:#f0e0e0;" !9 \|{{CDD\|node\|4\|node\|3\|node\|3\|node\|3\|node_1\|3\|node\|3\|node_1}} t_0,2{3,3,3,3,3,4}	Cantellated 7-orthoplex (Sarz)	\|(0,0,0,0,1,1,2)√2	226	4200	15456	24080	19320	7560	840
style="text-align:center; background:#f0e0e0;" !10 \|{{CDD\|node\|4\|node\|3\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node}} t_1,2{3,3,3,3,3,4}	Bitruncated 7-orthoplex (Botaz)	\|(0,0,0,0,1,2,2)√2						4200	840
style="text-align:center; background:#f0e0e0;" !11 \|{{CDD\|node\|4\|node\|3\|node\|3\|node_1\|3\|node\|3\|node\|3\|node_1}} t_0,3{3,3,3,3,3,4}	Runcinated 7-orthoplex (Spaz)	\|(0,0,0,1,1,1,2)√2						23520	2240
style="text-align:center; background:#f0e0e0;" !12 \|{{CDD\|node\|4\|node\|3\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node}} t_1,3{3,3,3,3,3,4}	Bicantellated 7-orthoplex (Sebraz)	\|(0,0,0,1,1,2,2)√2						26880	3360
style="text-align:center; background:#f0e0e0;" !13 \|{{CDD\|node\|4\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node}} t_2,3{3,3,3,3,3,4}	Tritruncated 7-orthoplex (Totaz)	\|(0,0,0,1,2,2,2)√2						10080	2240
style="text-align:center; background:#f0e0e0;" !14 \|{{CDD\|node\|4\|node\|3\|node_1\|3\|node\|3\|node\|3\|node\|3\|node_1}} t_0,4{3,3,3,3,3,4}	Stericated 7-orthoplex (Scaz)	\|(0,0,1,1,1,1,2)√2						33600	3360
style="text-align:center; background:#f0e0e0;" !15 \|{{CDD\|node\|4\|node\|3\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node}} t_1,4{3,3,3,3,3,4}	Biruncinated 7-orthoplex (Sibpaz)	\|(0,0,1,1,1,2,2)√2						60480	6720
style="text-align:center; background:#e0f0e0;" !16 \|{{CDD\|node\|4\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node}} t_2,4{4,3,3,3,3,3}	Tricantellated 7-cube (Strasaz)	\|(0,0,1,1,2,2,2)√2						47040	6720
style="text-align:center; background:#e0e0f0;" !17 \|{{CDD\|node\|4\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node\|3\|node}} t_2,3{4,3,3,3,3,3}	Tritruncated 7-cube (Tatsa)	\|(0,0,1,2,2,2,2)√2						13440	3360
style="text-align:center; background:#f0e0e0;" !18 \|{{CDD\|node\|4\|node_1\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node_1}} t_0,5{3,3,3,3,3,4}	Pentellated 7-orthoplex (Staz)	\|(0,1,1,1,1,1,2)√2						20160	2688
style="text-align:center; background:#e0f0e0;" !19 \|{{CDD\|node\|4\|node_1\|3\|node\|3\|node\|3\|node\|3\|node_1\|3\|node}} t_1,5{4,3,3,3,3,3}	Bistericated 7-cube (Sabcosaz)	\|(0,1,1,1,1,2,2)√2						53760	6720
style="text-align:center; background:#e0e0f0;" !20 \|{{CDD\|node\|4\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node\|3\|node}} t_1,4{4,3,3,3,3,3}	Biruncinated 7-cube (Sibposa)	\|(0,1,1,1,2,2,2)√2						67200	8960
style="text-align:center; background:#e0e0f0;" !21 \|{{CDD\|node\|4\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node\|3\|node}} t_1,3{4,3,3,3,3,3}	Bicantellated 7-cube (Sibrosa)	\|(0,1,1,2,2,2,2)√2						40320	6720
style="text-align:center; background:#e0e0f0;" !22 \|{{CDD\|node\|4\|node_1\|3\|node_1\|3\|node\|3\|node\|3\|node\|3\|node}} t_1,2{4,3,3,3,3,3}	Bitruncated 7-cube (Betsa)	\|(0,1,2,2,2,2,2)√2						9408	2688
style="text-align:center; background:#e0f0e0;" !23 \|{{CDD\|node_1\|4\|node\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node_1}} t_0,6{4,3,3,3,3,3}	Hexicated 7-cube (Supposaz)	\|(0,0,0,0,0,0,1)√2 + (1,1,1,1,1,1,1)						5376	896
style="text-align:center; background:#e0e0f0;" !24 \|{{CDD\|node_1\|4\|node\|3\|node\|3\|node\|3\|node\|3\|node_1\|3\|node}} t_0,5{4,3,3,3,3,3}	Pentellated 7-cube (Stesa)	\|(0,0,0,0,0,1,1)√2 + (1,1,1,1,1,1,1)						20160	2688
style="text-align:center; background:#e0e0f0;" !25 \|{{CDD\|node_1\|4\|node\|3\|node\|3\|node\|3\|node_1\|3\|node\|3\|node}} t_0,4{4,3,3,3,3,3}	Stericated 7-cube (Scosa)	\|(0,0,0,0,1,1,1)√2 + (1,1,1,1,1,1,1)						35840	4480
style="text-align:center; background:#e0e0f0;" !26 \|{{CDD\|node_1\|4\|node\|3\|node\|3\|node_1\|3\|node\|3\|node\|3\|node}} t_0,3{4,3,3,3,3,3}	Runcinated 7-cube (Spesa)	\|(0,0,0,1,1,1,1)√2 + (1,1,1,1,1,1,1)						33600	4480
style="text-align:center; background:#e0e0f0;" !27 \|{{CDD\|node_1\|4\|node\|3\|node_1\|3\|node\|3\|node\|3\|node\|3\|node}} t_0,2{4,3,3,3,3,3}	Cantellated 7-cube (Sersa)	\|(0,0,1,1,1,1,1)√2 + (1,1,1,1,1,1,1)						16128	2688
style="text-align:center; background:#e0e0f0;" !28 \|{{CDD\|node_1\|4\|node_1\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node}} t_0,1{4,3,3,3,3,3}	Truncated 7-cube (Tasa)	\|(0,1,1,1,1,1,1)√2 + (1,1,1,1,1,1,1)	142	980	2968	5040	5152	3136	896
style="text-align:center; background:#f0e0e0;" !29 \|{{CDD\|node\|4\|node\|3\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1}} t_0,1,2{3,3,3,3,3,4}	Cantitruncated 7-orthoplex (Garz)	\|(0,1,2,3,3,3,3)√2						8400	1680
style="text-align:center; background:#f0e0e0;" !30 \|{{CDD\|node\|4\|node\|3\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1}} t_0,1,3{3,3,3,3,3,4}	Runcitruncated 7-orthoplex (Potaz)	\|(0,1,2,2,3,3,3)√2						50400	6720
style="text-align:center; background:#f0e0e0;" !31 \|{{CDD\|node\|4\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1}} t_0,2,3{3,3,3,3,3,4}	Runcicantellated 7-orthoplex (Parz)	\|(0,1,1,2,3,3,3)√2						33600	6720
style="text-align:center; background:#f0e0e0;" !32 \|{{CDD\|node\|4\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node}} t_1,2,3{3,3,3,3,3,4}	Bicantitruncated 7-orthoplex (Gebraz)	\|(0,0,1,2,3,3,3)√2						30240	6720
style="text-align:center; background:#f0e0e0;" !33 \|{{CDD\|node\|4\|node\|3\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node_1}} t_0,1,4{3,3,3,3,3,4}	Steritruncated 7-orthoplex (Catz)	\|(0,0,1,1,1,2,3)√2						107520	13440
style="text-align:center; background:#f0e0e0;" !34 \|{{CDD\|node\|4\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node_1}} t_0,2,4{3,3,3,3,3,4}	Stericantellated 7-orthoplex (Craze)	\|(0,0,1,1,2,2,3)√2						141120	20160
style="text-align:center; background:#f0e0e0;" !35 \|{{CDD\|node\|4\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node}} t_1,2,4{3,3,3,3,3,4}	Biruncitruncated 7-orthoplex (Baptize)	\|(0,0,1,1,2,3,3)√2						120960	20160
style="text-align:center; background:#f0e0e0;" !36 \|{{CDD\|node\|4\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node\|3\|node_1}} t_0,3,4{3,3,3,3,3,4}	Steriruncinated 7-orthoplex (Copaz)	\|(0,1,1,1,2,3,3)√2						67200	13440
style="text-align:center; background:#f0e0e0;" !37 \|{{CDD\|node\|4\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node}} t_1,3,4{3,3,3,3,3,4}	Biruncicantellated 7-orthoplex (Boparz)	\|(0,0,1,2,2,3,3)√2						100800	20160
style="text-align:center; background:#e0f0e0;" !38 \|{{CDD\|node\|4\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node}} t_2,3,4{4,3,3,3,3,3}	Tricantitruncated 7-cube (Gotrasaz)	\|(0,0,0,1,2,3,3)√2						53760	13440
style="text-align:center; background:#f0e0e0;" !39 \|{{CDD\|node\|4\|node_1\|3\|node\|3\|node\|3\|node\|3\|node_1\|3\|node_1}} t_0,1,5{3,3,3,3,3,4}	Pentitruncated 7-orthoplex (Tetaz)	\|(0,1,1,1,1,2,3)√2						87360	13440
style="text-align:center; background:#f0e0e0;" !40 \|{{CDD\|node\|4\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node\|3\|node_1}} t_0,2,5{3,3,3,3,3,4}	Penticantellated 7-orthoplex (Teroz)	\|(0,1,1,1,2,2,3)√2						188160	26880
style="text-align:center; background:#f0e0e0;" !41 \|{{CDD\|node\|4\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node}} t_1,2,5{3,3,3,3,3,4}	Bisteritruncated 7-orthoplex (Boctaz)	\|(0,1,1,1,2,3,3)√2						147840	26880
style="text-align:center; background:#f0e0e0;" !42 \|{{CDD\|node\|4\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node\|3\|node_1}} t_0,3,5{3,3,3,3,3,4}	Pentiruncinated 7-orthoplex (Topaz)	\|(0,1,1,2,2,2,3)√2						174720	26880
style="text-align:center; background:#e0f0e0;" !43 \|{{CDD\|node\|4\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node}} t_1,3,5{4,3,3,3,3,3}	Bistericantellated 7-cube (Bacresaz)	\|(0,1,1,2,2,3,3)√2						241920	40320
style="text-align:center; background:#e0e0f0;" !44 \|{{CDD\|node\|4\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node}} t_1,3,4{4,3,3,3,3,3}	Biruncicantellated 7-cube (Bopresa)	\|(0,1,1,2,3,3,3)√2						120960	26880
style="text-align:center; background:#f0e0e0;" !45 \|{{CDD\|node\|4\|node_1\|3\|node_1\|3\|node\|3\|node\|3\|node\|3\|node_1}} t_0,4,5{3,3,3,3,3,4}	Pentistericated 7-orthoplex (Tocaz)	\|(0,1,2,2,2,2,3)√2						67200	13440
style="text-align:center; background:#e0e0f0;" !46 \|{{CDD\|node\|4\|node_1\|3\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node}} t_1,2,5{4,3,3,3,3,3}	Bisteritruncated 7-cube (Bactasa)	\|(0,1,2,2,2,3,3)√2						147840	26880
style="text-align:center; background:#e0e0f0;" !47 \|{{CDD\|node\|4\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node}} t_1,2,4{4,3,3,3,3,3}	Biruncitruncated 7-cube (Biptesa)	\|(0,1,2,2,3,3,3)√2						134400	26880
style="text-align:center; background:#e0e0f0;" !48 \|{{CDD\|node\|4\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node\|3\|node}} t_1,2,3{4,3,3,3,3,3}	Bicantitruncated 7-cube (Gibrosa)	\|(0,1,2,3,3,3,3)√2						47040	13440
style="text-align:center; background:#f0e0e0;" !49 \|{{CDD\|node_1\|4\|node\|3\|node\|3\|node\|3\|node\|3\|node_1\|3\|node_1}} t_0,1,6{3,3,3,3,3,4}	Hexitruncated 7-orthoplex (Putaz)	\|(0,0,0,0,0,1,2)√2 + (1,1,1,1,1,1,1)						29568	5376
style="text-align:center; background:#f0e0e0;" !50 \|{{CDD\|node_1\|4\|node\|3\|node\|3\|node\|3\|node_1\|3\|node\|3\|node_1}} t_0,2,6{3,3,3,3,3,4}	Hexicantellated 7-orthoplex (Puraz)	\|(0,0,0,0,1,1,2)√2 + (1,1,1,1,1,1,1)						94080	13440
style="text-align:center; background:#e0e0f0;" !51 \|{{CDD\|node_1\|4\|node\|3\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node}} t_0,4,5{4,3,3,3,3,3}	Pentistericated 7-cube (Tacosa)	\|(0,0,0,0,1,2,2)√2 + (1,1,1,1,1,1,1)						67200	13440
style="text-align:center; background:#e0f0e0;" !52 \|{{CDD\|node_1\|4\|node\|3\|node\|3\|node_1\|3\|node\|3\|node\|3\|node_1}} t_0,3,6{4,3,3,3,3,3}	Hexiruncinated 7-cube (Pupsez)	\|(0,0,0,1,1,1,2)√2 + (1,1,1,1,1,1,1)						134400	17920
style="text-align:center; background:#e0e0f0;" !53 \|{{CDD\|node_1\|4\|node\|3\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node}} t_0,3,5{4,3,3,3,3,3}	Pentiruncinated 7-cube (Tapsa)	\|(0,0,0,1,1,2,2)√2 + (1,1,1,1,1,1,1)						174720	26880
style="text-align:center; background:#e0e0f0;" !54 \|{{CDD\|node_1\|4\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node}} t_0,3,4{4,3,3,3,3,3}	Steriruncinated 7-cube (Capsa)	\|(0,0,0,1,2,2,2)√2 + (1,1,1,1,1,1,1)						80640	17920
style="text-align:center; background:#e0e0f0;" !55 \|{{CDD\|node_1\|4\|node\|3\|node_1\|3\|node\|3\|node\|3\|node\|3\|node_1}} t_0,2,6{4,3,3,3,3,3}	Hexicantellated 7-cube (Purosa)	\|(0,0,1,1,1,1,2)√2 + (1,1,1,1,1,1,1)						94080	13440
style="text-align:center; background:#e0e0f0;" !56 \|{{CDD\|node_1\|4\|node\|3\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node}} t_0,2,5{4,3,3,3,3,3}	Penticantellated 7-cube (Tersa)	\|(0,0,1,1,1,2,2)√2 + (1,1,1,1,1,1,1)						188160	26880
style="text-align:center; background:#e0e0f0;" !57 \|{{CDD\|node_1\|4\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node}} t_0,2,4{4,3,3,3,3,3}	Stericantellated 7-cube (Carsa)	\|(0,0,1,1,2,2,2)√2 + (1,1,1,1,1,1,1)						161280	26880
style="text-align:center; background:#e0e0f0;" !58 \|{{CDD\|node_1\|4\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node\|3\|node}} t_0,2,3{4,3,3,3,3,3}	Runcicantellated 7-cube (Parsa)	\|(0,0,1,2,2,2,2)√2 + (1,1,1,1,1,1,1)						53760	13440
style="text-align:center; background:#e0e0f0;" !59 \|{{CDD\|node_1\|4\|node_1\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node_1}} t_0,1,6{4,3,3,3,3,3}	Hexitruncated 7-cube (Putsa)	\|(0,1,1,1,1,1,2)√2 + (1,1,1,1,1,1,1)						29568	5376
style="text-align:center; background:#e0e0f0;" !60 \|{{CDD\|node_1\|4\|node_1\|3\|node\|3\|node\|3\|node\|3\|node_1\|3\|node}} t_0,1,5{4,3,3,3,3,3}	Pentitruncated 7-cube (Tetsa)	\|(0,1,1,1,1,2,2)√2 + (1,1,1,1,1,1,1)						87360	13440
style="text-align:center; background:#e0e0f0;" !61 \|{{CDD\|node_1\|4\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node\|3\|node}} t_0,1,4{4,3,3,3,3,3}	Steritruncated 7-cube (Catsa)	\|(0,1,1,1,2,2,2)√2 + (1,1,1,1,1,1,1)						116480	17920
style="text-align:center; background:#e0e0f0;" !62 \|{{CDD\|node_1\|4\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node\|3\|node}} t_0,1,3{4,3,3,3,3,3}	Runcitruncated 7-cube (Petsa)	\|(0,1,1,2,2,2,2)√2 + (1,1,1,1,1,1,1)						73920	13440
style="text-align:center; background:#e0e0f0;" !63 \|{{CDD\|node_1\|4\|node_1\|3\|node_1\|3\|node\|3\|node\|3\|node\|3\|node}} t_0,1,2{4,3,3,3,3,3}	Cantitruncated 7-cube (Gersa)	\|(0,1,2,2,2,2,2)√2 + (1,1,1,1,1,1,1)						18816	5376
style="text-align:center; background:#f0e0e0;" !64 \|{{CDD\|node\|4\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1}} t_0,1,2,3{3,3,3,3,3,4}	Runcicantitruncated 7-orthoplex (Gopaz)	\|(0,1,2,3,4,4,4)√2						60480	13440
style="text-align:center; background:#f0e0e0;" !65 \|{{CDD\|node\|4\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1}} t_0,1,2,4{3,3,3,3,3,4}	Stericantitruncated 7-orthoplex (Cogarz)	\|(0,0,1,1,2,3,4)√2						241920	40320
style="text-align:center; background:#f0e0e0;" !66 \|{{CDD\|node\|4\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1}} t_0,1,3,4{3,3,3,3,3,4}	Steriruncitruncated 7-orthoplex (Captaz)	\|(0,0,1,2,2,3,4)√2						181440	40320
style="text-align:center; background:#f0e0e0;" !67 \|{{CDD\|node\|4\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1}} t_0,2,3,4{3,3,3,3,3,4}	Steriruncicantellated 7-orthoplex (Caparz)	\|(0,0,1,2,3,3,4)√2						181440	40320
style="text-align:center; background:#f0e0e0;" !68 \|{{CDD\|node\|4\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node}} t_1,2,3,4{3,3,3,3,3,4}	Biruncicantitruncated 7-orthoplex (Gibpaz)	\|(0,0,1,2,3,4,4)√2						161280	40320
style="text-align:center; background:#f0e0e0;" !69 \|{{CDD\|node\|4\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1}} t_0,1,2,5{3,3,3,3,3,4}	Penticantitruncated 7-orthoplex (Tograz)	\|(0,1,1,1,2,3,4)√2						295680	53760
style="text-align:center; background:#f0e0e0;" !70 \|{{CDD\|node\|4\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1}} t_0,1,3,5{3,3,3,3,3,4}	Pentiruncitruncated 7-orthoplex (Toptaz)	\|(0,1,1,2,2,3,4)√2						443520	80640
style="text-align:center; background:#f0e0e0;" !71 \|{{CDD\|node\|4\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1}} t_0,2,3,5{3,3,3,3,3,4}	Pentiruncicantellated 7-orthoplex (Toparz)	\|(0,1,1,2,3,3,4)√2						403200	80640
style="text-align:center; background:#f0e0e0;" !72 \|{{CDD\|node\|4\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node}} t_1,2,3,5{3,3,3,3,3,4}	Bistericantitruncated 7-orthoplex (Becogarz)	\|(0,1,1,2,3,4,4)√2						362880	80640
style="text-align:center; background:#f0e0e0;" !73 \|{{CDD\|node\|4\|node_1\|3\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node_1}} t_0,1,4,5{3,3,3,3,3,4}	Pentisteritruncated 7-orthoplex (Tacotaz)	\|(0,1,2,2,2,3,4)√2						241920	53760
style="text-align:center; background:#f0e0e0;" !74 \|{{CDD\|node\|4\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node_1}} t_0,2,4,5{3,3,3,3,3,4}	Pentistericantellated 7-orthoplex (Tocarz)	\|(0,1,2,2,3,3,4)√2						403200	80640
style="text-align:center; background:#e0f0e0;" !75 \|{{CDD\|node\|4\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node}} t_1,2,4,5{4,3,3,3,3,3}	Bisteriruncitruncated 7-cube (Bocaptosaz)	\|(0,1,2,2,3,4,4)√2						322560	80640
style="text-align:center; background:#f0e0e0;" !76 \|{{CDD\|node\|4\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node\|3\|node_1}} t_0,3,4,5{3,3,3,3,3,4}	Pentisteriruncinated 7-orthoplex (Tecpaz)	\|(0,1,2,3,3,3,4)√2						241920	53760
style="text-align:center; background:#e0e0f0;" !77 \|{{CDD\|node\|4\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node}} t_1,2,3,5{4,3,3,3,3,3}	Bistericantitruncated 7-cube (Becgresa)	\|(0,1,2,3,3,4,4)√2						362880	80640
style="text-align:center; background:#e0e0f0;" !78 \|{{CDD\|node\|4\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node}} t_1,2,3,4{4,3,3,3,3,3}	Biruncicantitruncated 7-cube (Gibposa)	\|(0,1,2,3,4,4,4)√2						188160	53760
style="text-align:center; background:#f0e0e0;" !79 \|{{CDD\|node_1\|4\|node\|3\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1}} t_0,1,2,6{3,3,3,3,3,4}	Hexicantitruncated 7-orthoplex (Pugarez)	\|(0,0,0,0,1,2,3)√2 + (1,1,1,1,1,1,1)						134400	26880
style="text-align:center; background:#f0e0e0;" !80 \|{{CDD\|node_1\|4\|node\|3\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1}} t_0,1,3,6{3,3,3,3,3,4}	Hexiruncitruncated 7-orthoplex (Papataz)	\|(0,0,0,1,1,2,3)√2 + (1,1,1,1,1,1,1)						322560	53760
style="text-align:center; background:#f0e0e0;" !81 \|{{CDD\|node_1\|4\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1}} t_0,2,3,6{3,3,3,3,3,4}	Hexiruncicantellated 7-orthoplex (Puparez)	\|(0,0,0,1,2,2,3)√2 + (1,1,1,1,1,1,1)						268800	53760
style="text-align:center; background:#e0e0f0;" !82 \|{{CDD\|node_1\|4\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node}} t_0,3,4,5{4,3,3,3,3,3}	Pentisteriruncinated 7-cube (Tecpasa)	\|(0,0,0,1,2,3,3)√2 + (1,1,1,1,1,1,1)						241920	53760
style="text-align:center; background:#f0e0e0;" !83 \|{{CDD\|node_1\|4\|node\|3\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node_1}} t_0,1,4,6{3,3,3,3,3,4}	Hexisteritruncated 7-orthoplex (Pucotaz)	\|(0,0,1,1,1,2,3)√2 + (1,1,1,1,1,1,1)						322560	53760
style="text-align:center; background:#e0f0e0;" !84 \|{{CDD\|node_1\|4\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node_1}} t_0,2,4,6{4,3,3,3,3,3}	Hexistericantellated 7-cube (Pucrosaz)	\|(0,0,1,1,2,2,3)√2 + (1,1,1,1,1,1,1)						483840	80640
style="text-align:center; background:#e0e0f0;" !85 \|{{CDD\|node_1\|4\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node}} t_0,2,4,5{4,3,3,3,3,3}	Pentistericantellated 7-cube (Tecresa)	\|(0,0,1,1,2,3,3)√2 + (1,1,1,1,1,1,1)						403200	80640
style="text-align:center; background:#e0e0f0;" !86 \|{{CDD\|node_1\|4\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node\|3\|node_1}} t_0,2,3,6{4,3,3,3,3,3}	Hexiruncicantellated 7-cube (Pupresa)	\|(0,0,1,2,2,2,3)√2 + (1,1,1,1,1,1,1)						268800	53760
style="text-align:center; background:#e0e0f0;" !87 \|{{CDD\|node_1\|4\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node}} t_0,2,3,5{4,3,3,3,3,3}	Pentiruncicantellated 7-cube (Topresa)	\|(0,0,1,2,2,3,3)√2 + (1,1,1,1,1,1,1)						403200	80640
style="text-align:center; background:#e0e0f0;" !88 \|{{CDD\|node_1\|4\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node}} t_0,2,3,4{4,3,3,3,3,3}	Steriruncicantellated 7-cube (Copresa)	\|(0,0,1,2,3,3,3)√2 + (1,1,1,1,1,1,1)						215040	53760
style="text-align:center; background:#e0f0e0;" !89 \|{{CDD\|node_1\|4\|node_1\|3\|node\|3\|node\|3\|node\|3\|node_1\|3\|node_1}} t_0,1,5,6{4,3,3,3,3,3}	Hexipentitruncated 7-cube (Putatosez)	\|(0,1,1,1,1,2,3)√2 + (1,1,1,1,1,1,1)						134400	26880
style="text-align:center; background:#e0e0f0;" !90 \|{{CDD\|node_1\|4\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node\|3\|node_1}} t_0,1,4,6{4,3,3,3,3,3}	Hexisteritruncated 7-cube (Pacutsa)	\|(0,1,1,1,2,2,3)√2 + (1,1,1,1,1,1,1)						322560	53760
style="text-align:center; background:#e0e0f0;" !91 \|{{CDD\|node_1\|4\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node}} t_0,1,4,5{4,3,3,3,3,3}	Pentisteritruncated 7-cube (Tecatsa)	\|(0,1,1,1,2,3,3)√2 + (1,1,1,1,1,1,1)						241920	53760
style="text-align:center; background:#e0e0f0;" !92 \|{{CDD\|node_1\|4\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node\|3\|node_1}} t_0,1,3,6{4,3,3,3,3,3}	Hexiruncitruncated 7-cube (Pupetsa)	\|(0,1,1,2,2,2,3)√2 + (1,1,1,1,1,1,1)						322560	53760
style="text-align:center; background:#e0e0f0;" !93 \|{{CDD\|node_1\|4\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node}} t_0,1,3,5{4,3,3,3,3,3}	Pentiruncitruncated 7-cube (Toptosa)	\|(0,1,1,2,2,3,3)√2 + (1,1,1,1,1,1,1)						443520	80640
style="text-align:center; background:#e0e0f0;" !94 \|{{CDD\|node_1\|4\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node}} t_0,1,3,4{4,3,3,3,3,3}	Steriruncitruncated 7-cube (Captesa)	\|(0,1,1,2,3,3,3)√2 + (1,1,1,1,1,1,1)						215040	53760
style="text-align:center; background:#e0e0f0;" !95 \|{{CDD\|node_1\|4\|node_1\|3\|node_1\|3\|node\|3\|node\|3\|node\|3\|node_1}} t_0,1,2,6{4,3,3,3,3,3}	Hexicantitruncated 7-cube (Pugrosa)	\|(0,1,2,2,2,2,3)√2 + (1,1,1,1,1,1,1)						134400	26880
style="text-align:center; background:#e0e0f0;" !96 \|{{CDD\|node_1\|4\|node_1\|3\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node}} t_0,1,2,5{4,3,3,3,3,3}	Penticantitruncated 7-cube (Togresa)	\|(0,1,2,2,2,3,3)√2 + (1,1,1,1,1,1,1)						295680	53760
style="text-align:center; background:#e0e0f0;" !97 \|{{CDD\|node_1\|4\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node}} t_0,1,2,4{4,3,3,3,3,3}	Stericantitruncated 7-cube (Cogarsa)	\|(0,1,2,2,3,3,3)√2 + (1,1,1,1,1,1,1)						268800	53760
style="text-align:center; background:#e0e0f0;" !98 \|{{CDD\|node_1\|4\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node\|3\|node}} t_0,1,2,3{4,3,3,3,3,3}	Runcicantitruncated 7-cube (Gapsa)	\|(0,1,2,3,3,3,3)√2 + (1,1,1,1,1,1,1)						94080	26880
style="text-align:center; background:#f0e0e0;" !99 \|{{CDD\|node\|4\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1}} t_0,1,2,3,4{3,3,3,3,3,4}	Steriruncicantitruncated 7-orthoplex (Gocaz)	\|(0,0,1,2,3,4,5)√2						322560	80640
style="text-align:center; background:#f0e0e0;" !100 \|{{CDD\|node\|4\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1}} t_0,1,2,3,5{3,3,3,3,3,4}	Pentiruncicantitruncated 7-orthoplex (Tegopaz)	\|(0,1,1,2,3,4,5)√2						725760	161280
style="text-align:center; background:#f0e0e0;" !101 \|{{CDD\|node\|4\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1}} t_0,1,2,4,5{3,3,3,3,3,4}	Pentistericantitruncated 7-orthoplex (Tecagraz)	\|(0,1,2,2,3,4,5)√2						645120	161280
style="text-align:center; background:#f0e0e0;" !102 \|{{CDD\|node\|4\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1}} t_0,1,3,4,5{3,3,3,3,3,4}	Pentisteriruncitruncated 7-orthoplex (Tecpotaz)	\|(0,1,2,3,3,4,5)√2						645120	161280
style="text-align:center; background:#f0e0e0;" !103 \|{{CDD\|node\|4\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1}} t_0,2,3,4,5{3,3,3,3,3,4}	Pentisteriruncicantellated 7-orthoplex (Tacparez)	\|(0,1,2,3,4,4,5)√2						645120	161280
style="text-align:center; background:#e0f0e0;" !104 \|{{CDD\|node\|4\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node}} t_1,2,3,4,5{4,3,3,3,3,3}	Bisteriruncicantitruncated 7-cube (Gabcosaz)	\|(0,1,2,3,4,5,5)√2						564480	161280
style="text-align:center; background:#f0e0e0;" !105 \|{{CDD\|node_1\|4\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1}} t_0,1,2,3,6{3,3,3,3,3,4}	Hexiruncicantitruncated 7-orthoplex (Pugopaz)	\|(0,0,0,1,2,3,4)√2 + (1,1,1,1,1,1,1)						483840	107520
style="text-align:center; background:#f0e0e0;" !106 \|{{CDD\|node_1\|4\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1}} t_0,1,2,4,6{3,3,3,3,3,4}	Hexistericantitruncated 7-orthoplex (Pucagraz)	\|(0,0,1,1,2,3,4)√2 + (1,1,1,1,1,1,1)						806400	161280
style="text-align:center; background:#f0e0e0;" !107 \|{{CDD\|node_1\|4\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1}} t_0,1,3,4,6{3,3,3,3,3,4}	Hexisteriruncitruncated 7-orthoplex (Pucpotaz)	\|(0,0,1,2,2,3,4)√2 + (1,1,1,1,1,1,1)						725760	161280
style="text-align:center; background:#e0f0e0;" !108 \|{{CDD\|node_1\|4\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1}} t_0,2,3,4,6{4,3,3,3,3,3}	Hexisteriruncicantellated 7-cube (Pucprosaz)	\|(0,0,1,2,3,3,4)√2 + (1,1,1,1,1,1,1)						725760	161280
style="text-align:center; background:#e0e0f0;" !109 \|{{CDD\|node_1\|4\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node}} t_0,2,3,4,5{4,3,3,3,3,3}	Pentisteriruncicantellated 7-cube (Tocpresa)	\|(0,0,1,2,3,4,4)√2 + (1,1,1,1,1,1,1)						645120	161280
style="text-align:center; background:#f0e0e0;" !110 \|{{CDD\|node_1\|4\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1}} t_0,1,2,5,6{3,3,3,3,3,4}	Hexipenticantitruncated 7-orthoplex (Putegraz)	\|(0,1,1,1,2,3,4)√2 + (1,1,1,1,1,1,1)						483840	107520
style="text-align:center; background:#e0f0e0;" !111 \|{{CDD\|node_1\|4\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1}} t_0,1,3,5,6{4,3,3,3,3,3}	Hexipentiruncitruncated 7-cube (Putpetsaz)	\|(0,1,1,2,2,3,4)√2 + (1,1,1,1,1,1,1)						806400	161280
style="text-align:center; background:#e0e0f0;" !112 \|{{CDD\|node_1\|4\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1}} t_0,1,3,4,6{4,3,3,3,3,3}	Hexisteriruncitruncated 7-cube (Pucpetsa)	\|(0,1,1,2,3,3,4)√2 + (1,1,1,1,1,1,1)						725760	161280
style="text-align:center; background:#e0e0f0;" !113 \|{{CDD\|node_1\|4\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node}} t_0,1,3,4,5{4,3,3,3,3,3}	Pentisteriruncitruncated 7-cube (Tecpetsa)	\|(0,1,1,2,3,4,4)√2 + (1,1,1,1,1,1,1)						645120	161280
style="text-align:center; background:#e0e0f0;" !114 \|{{CDD\|node_1\|4\|node_1\|3\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node_1}} t_0,1,2,5,6{4,3,3,3,3,3}	Hexipenticantitruncated 7-cube (Putgresa)	\|(0,1,2,2,2,3,4)√2 + (1,1,1,1,1,1,1)						483840	107520
style="text-align:center; background:#e0e0f0;" !115 \|{{CDD\|node_1\|4\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node_1}} t_0,1,2,4,6{4,3,3,3,3,3}	Hexistericantitruncated 7-cube (Pucagrosa)	\|(0,1,2,2,3,3,4)√2 + (1,1,1,1,1,1,1)						806400	161280
style="text-align:center; background:#e0e0f0;" !116 \|{{CDD\|node_1\|4\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node}} t_0,1,2,4,5{4,3,3,3,3,3}	Pentistericantitruncated 7-cube (Tecgresa)	\|(0,1,2,2,3,4,4)√2 + (1,1,1,1,1,1,1)						645120	161280
style="text-align:center; background:#e0e0f0;" !117 \|{{CDD\|node_1\|4\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node\|3\|node_1}} t_0,1,2,3,6{4,3,3,3,3,3}	Hexiruncicantitruncated 7-cube (Pugopsa)	\|(0,1,2,3,3,3,4)√2 + (1,1,1,1,1,1,1)						483840	107520
style="text-align:center; background:#e0e0f0;" !118 \|{{CDD\|node_1\|4\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node}} t_0,1,2,3,5{4,3,3,3,3,3}	Pentiruncicantitruncated 7-cube (Togapsa)	\|(0,1,2,3,3,4,4)√2 + (1,1,1,1,1,1,1)						725760	161280
style="text-align:center; background:#e0e0f0;" !119 \|{{CDD\|node_1\|4\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node}} t_0,1,2,3,4{4,3,3,3,3,3}	Steriruncicantitruncated 7-cube (Gacosa)	\|(0,1,2,3,4,4,4)√2 + (1,1,1,1,1,1,1)						376320	107520
style="text-align:center; background:#f0e0e0;" !120 \|{{CDD\|node\|4\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1}} t_0,1,2,3,4,5{3,3,3,3,3,4}	Pentisteriruncicantitruncated 7-orthoplex (Gotaz)	\|(0,1,2,3,4,5,6)√2						1128960	322560
style="text-align:center; background:#f0e0e0;" !121 \|{{CDD\|node_1\|4\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1}} t_0,1,2,3,4,6{3,3,3,3,3,4}	Hexisteriruncicantitruncated 7-orthoplex (Pugacaz)	\|(0,0,1,2,3,4,5)√2 + (1,1,1,1,1,1,1)						1290240	322560
style="text-align:center; background:#f0e0e0;" !122 \|{{CDD\|node_1\|4\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1}} t_0,1,2,3,5,6{3,3,3,3,3,4}	Hexipentiruncicantitruncated 7-orthoplex (Putgapaz)	\|(0,1,1,2,3,4,5)√2 + (1,1,1,1,1,1,1)						1290240	322560
style="text-align:center; background:#e0f0e0;" !123 \|{{CDD\|node_1\|4\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1}} t_0,1,2,4,5,6{4,3,3,3,3,3}	Hexipentistericantitruncated 7-cube (Putcagrasaz)	\|(0,1,2,2,3,4,5)√2 + (1,1,1,1,1,1,1)						1290240	322560
style="text-align:center; background:#e0e0f0;" !124 \|{{CDD\|node_1\|4\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1}} t_0,1,2,3,5,6{4,3,3,3,3,3}	Hexipentiruncicantitruncated 7-cube (Putgapsa)	\|(0,1,2,3,3,4,5)√2 + (1,1,1,1,1,1,1)						1290240	322560
style="text-align:center; background:#e0e0f0;" !125 \|{{CDD\|node_1\|4\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1}} t_0,1,2,3,4,6{4,3,3,3,3,3}	Hexisteriruncicantitruncated 7-cube (Pugacasa)	\|(0,1,2,3,4,4,5)√2 + (1,1,1,1,1,1,1)						1290240	322560
style="text-align:center; background:#e0e0f0;" !126 \|{{CDD\|node_1\|4\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node}} t_0,1,2,3,4,5{4,3,3,3,3,3}	Pentisteriruncicantitruncated 7-cube (Gotesa)	\|(0,1,2,3,4,5,5)√2 + (1,1,1,1,1,1,1)						1128960	322560
style="text-align:center; background:#e0f0e0;" !127 \|{{CDD\|node_1\|4\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1}} t_{0,1,2,3,4,5,6}{4,3,3,3,3,3}	Omnitruncated 7-cube (Guposaz)	\|(0,1,2,3,4,5,6)√2 + (1,1,1,1,1,1,1)						2257920	645120

The D7 family

The D₇ family has symmetry of order 322560 (7 factorial x 2⁶).

This family has 3×32−1=95 Wythoffian uniform polytopes, generated by marking one or more nodes of the D₇ Coxeter-Dynkin diagram. Of these, 63 (2×32−1) are repeated from the B₇ family and 32 are unique to this family, listed below. Bowers names and acronym are given for cross-referencing.

See also list of D7 polytopes for Coxeter plane graphs of these polytopes.

rowspan=2\|# !rowspan=2\|Coxeter diagram !rowspan=2\|Names !rowspan=2\|Base point (Alternately signed) !colspan=7\|Element counts
class="wikitable collapsible collapsed" !colspan=12\|D₇ uniform polytopes
6\|\|5\|\|4\|\|3\|\|2\|\|1\|\|0
align=center !1	{{CDD\|nodes_10ru\|split2\|node\|3\|node\|3\|node\|3\|node\|3\|node}} = {{CDD\|node_h1\|4\|node\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node}}	7-cube demihepteract (hesa)	(1,1,1,1,1,1,1)	78	532	1624	2800	2240	672	64
align=center !2	{{CDD\|nodes_10ru\|split2\|node_1\|3\|node\|3\|node\|3\|node\|3\|node}} = {{CDD\|node_h1\|4\|node\|3\|node_1\|3\|node\|3\|node\|3\|node\|3\|node}}	cantic 7-cube truncated demihepteract (thesa)	(1,1,3,3,3,3,3)	142	1428	5656	11760	13440	7392	1344
align=center !3	{{CDD\|nodes_10ru\|split2\|node\|3\|node_1\|3\|node\|3\|node\|3\|node}} = {{CDD\|node_h1\|4\|node\|3\|node\|3\|node_1\|3\|node\|3\|node\|3\|node}}	runcic 7-cube small rhombated demihepteract (sirhesa)	(1,1,1,3,3,3,3)						16800	2240
align=center !4	{{CDD\|nodes_10ru\|split2\|node\|3\|node\|3\|node_1\|3\|node\|3\|node}} = {{CDD\|node_h1\|4\|node\|3\|node\|3\|node\|3\|node_1\|3\|node\|3\|node}}	steric 7-cube small prismated demihepteract (sphosa)	(1,1,1,1,3,3,3)						20160	2240
align=center !5	{{CDD\|nodes_10ru\|split2\|node\|3\|node\|3\|node\|3\|node_1\|3\|node}} = {{CDD\|node_h1\|4\|node\|3\|node\|3\|node\|3\|node\|3\|node_1\|3\|node}}	pentic 7-cube small cellated demihepteract (sochesa)	(1,1,1,1,1,3,3)						13440	1344
align=center !6	{{CDD\|nodes_10ru\|split2\|node\|3\|node\|3\|node\|3\|node\|3\|node_1}} = {{CDD\|node_h1\|4\|node\|3\|node\|3\|node\|3\|node\|3\|node\|3\|node_1}}	hexic 7-cube small terated demihepteract (suthesa)	(1,1,1,1,1,1,3)						4704	448
align=center !7	{{CDD\|nodes_10ru\|split2\|node_1\|3\|node_1\|3\|node\|3\|node\|3\|node}} = {{CDD\|node_h1\|4\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node\|3\|node}}	runcicantic 7-cube great rhombated demihepteract (Girhesa)	(1,1,3,5,5,5,5)						23520	6720
align=center !8	{{CDD\|nodes_10ru\|split2\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node}} = {{CDD\|node_h1\|4\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node}}	stericantic 7-cube prismatotruncated demihepteract (pothesa)	(1,1,3,3,5,5,5)						73920	13440
align=center !9	{{CDD\|nodes_10ru\|split2\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node}} = {{CDD\|node_h1\|4\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node}}	steriruncic 7-cube prismatorhomated demihepteract (prohesa)	(1,1,1,3,5,5,5)						40320	8960
align=center !10	{{CDD\|nodes_10ru\|split2\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node}} = {{CDD\|node_h1\|4\|node\|3\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node}}	penticantic 7-cube cellitruncated demihepteract (cothesa)	(1,1,3,3,3,5,5)						87360	13440
align=center !11	{{CDD\|nodes_10ru\|split2\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node}} = {{CDD\|node_h1\|4\|node\|3\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node}}	pentiruncic 7-cube cellirhombated demihepteract (crohesa)	(1,1,1,3,3,5,5)						87360	13440
align=center !12	{{CDD\|nodes_10ru\|split2\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node}} = {{CDD\|node_h1\|4\|node\|3\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node}}	pentisteric 7-cube celliprismated demihepteract (caphesa)	(1,1,1,1,3,5,5)						40320	6720
align=center !13	{{CDD\|nodes_10ru\|split2\|node_1\|3\|node\|3\|node\|3\|node\|3\|node_1}} = {{CDD\|node_h1\|4\|node\|3\|node_1\|3\|node\|3\|node\|3\|node\|3\|node_1}}	hexicantic 7-cube tericantic demihepteract (tuthesa)	(1,1,3,3,3,3,5)						43680	6720
align=center !14	{{CDD\|nodes_10ru\|split2\|node\|3\|node_1\|3\|node\|3\|node\|3\|node_1}} = {{CDD\|node_h1\|4\|node\|3\|node\|3\|node_1\|3\|node\|3\|node\|3\|node_1}}	hexiruncic 7-cube terirhombated demihepteract (turhesa)	(1,1,1,3,3,3,5)						67200	8960
align=center !15	{{CDD\|nodes_10ru\|split2\|node\|3\|node\|3\|node_1\|3\|node\|3\|node_1}} = {{CDD\|node_h1\|4\|node\|3\|node\|3\|node\|3\|node_1\|3\|node\|3\|node_1}}	hexisteric 7-cube teriprismated demihepteract (tuphesa)	(1,1,1,1,3,3,5)						53760	6720
align=center !16	{{CDD\|nodes_10ru\|split2\|node\|3\|node\|3\|node\|3\|node_1\|3\|node_1}} = {{CDD\|node_h1\|4\|node\|3\|node\|3\|node\|3\|node\|3\|node_1\|3\|node_1}}	hexipentic 7-cube tericellated demihepteract (tuchesa)	(1,1,1,1,1,3,5)						21504	2688
align=center !17	{{CDD\|nodes_10ru\|split2\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node}} = {{CDD\|node_h1\|4\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node}}	steriruncicantic 7-cube great prismated demihepteract (Gephosa)	(1,1,3,5,7,7,7)						94080	26880
align=center !18	{{CDD\|nodes_10ru\|split2\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node}} = {{CDD\|node_h1\|4\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node}}	pentiruncicantic 7-cube celligreatorhombated demihepteract (cagrohesa)	(1,1,3,5,5,7,7)						181440	40320
align=center !19	{{CDD\|nodes_10ru\|split2\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node}} = {{CDD\|node_h1\|4\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node}}	pentistericantic 7-cube celliprismatotruncated demihepteract (capthesa)	(1,1,3,3,5,7,7)						181440	40320
align=center !20	{{CDD\|nodes_10ru\|split2\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node}} = {{CDD\|node_h1\|4\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node}}	pentisteriruncic 7-cube celliprismatorhombated demihepteract (coprahesa)	(1,1,1,3,5,7,7)						120960	26880
align=center !21	{{CDD\|nodes_10ru\|split2\|node_1\|3\|node_1\|3\|node\|3\|node\|3\|node_1}} = {{CDD\|node_h1\|4\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node\|3\|node_1}}	hexiruncicantic 7-cube terigreatorhombated demihepteract (tugrohesa)	(1,1,3,5,5,5,7)						120960	26880
align=center !22	{{CDD\|nodes_10ru\|split2\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node_1}} = {{CDD\|node_h1\|4\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node\|3\|node_1}}	hexistericantic 7-cube teriprismatotruncated demihepteract (tupthesa)	(1,1,3,3,5,5,7)						221760	40320
align=center !23	{{CDD\|nodes_10ru\|split2\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1}} = {{CDD\|node_h1\|4\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1}}	hexisteriruncic 7-cube teriprismatorhombated demihepteract (tuprohesa)	(1,1,1,3,5,5,7)						134400	26880
align=center !24	{{CDD\|nodes_10ru\|split2\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node_1}} = {{CDD\|node_h1\|4\|node\|3\|node_1\|3\|node\|3\|node\|3\|node_1\|3\|node_1}}	hexipenticantic 7-cube teriCellitruncated demihepteract (tucothesa)	(1,1,3,3,3,5,7)						147840	26880
align=center !25	{{CDD\|nodes_10ru\|split2\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1}} = {{CDD\|node_h1\|4\|node\|3\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1}}	hexipentiruncic 7-cube tericellirhombated demihepteract (tucrohesa)	(1,1,1,3,3,5,7)						161280	26880
align=center !26	{{CDD\|nodes_10ru\|split2\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1}} = {{CDD\|node_h1\|4\|node\|3\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1}}	hexipentisteric 7-cube tericelliprismated demihepteract (tucophesa)	(1,1,1,1,3,5,7)						80640	13440
align=center !27	{{CDD\|nodes_10ru\|split2\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node}} = {{CDD\|node_h1\|4\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node}}	pentisteriruncicantic 7-cube great cellated demihepteract (gochesa)	(1,1,3,5,7,9,9)						282240	80640
align=center !28	{{CDD\|nodes_10ru\|split2\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1}} = {{CDD\|node_h1\|4\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1}}	hexisteriruncicantic 7-cube terigreatoprimated demihepteract (tugphesa)	(1,1,3,5,7,7,9)						322560	80640
align=center !29	{{CDD\|nodes_10ru\|split2\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1}} = {{CDD\|node_h1\|4\|node\|3\|node_1\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1}}	hexipentiruncicantic 7-cube tericelligreatorhombated demihepteract (tucagrohesa)	(1,1,3,5,5,7,9)						322560	80640
align=center !30	{{CDD\|nodes_10ru\|split2\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1}} = {{CDD\|node_h1\|4\|node\|3\|node_1\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1}}	hexipentistericantic 7-cube tericelliprismatotruncated demihepteract (tucpathesa)	(1,1,3,3,5,7,9)						362880	80640
align=center !31	{{CDD\|nodes_10ru\|split2\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1}} = {{CDD\|node_h1\|4\|node\|3\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1}}	hexipentisteriruncic 7-cube tericellprismatorhombated demihepteract (tucprohesa)	(1,1,1,3,5,7,9)						241920	53760
align=center !32	{{CDD\|nodes_10ru\|split2\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1}} = {{CDD\|node_h1\|4\|node\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1\|3\|node_1}}	hexipentisteriruncicantic 7-cube great terated demihepteract (guthesa)	(1,1,3,5,7,9,11)						564480	161280

The E7 family

The E₇ Coxeter group has order 2,903,040.

There are 127 forms based on all permutations of the Coxeter-Dynkin diagrams with one or more rings.

See also a list of E7 polytopes for symmetric Coxeter plane graphs of these polytopes.

rowspan=2\|# !rowspan=2\|Coxeter-Dynkin diagram Schläfli symbol !rowspan=2\|Names !colspan=7\|Element counts
class="wikitable collapsible collapsed" !colspan=12\|E₇ uniform polytopes
6\|\| 5\|\| 4\|\| 3\|\| 2\|\| 1\|\| 0
style="text-align:center;" \|1	{{CDD\|nodea\|3a\|nodea\|3a\|nodea\|3a\|branch\|3a\|nodea\|3a\|nodea_1}}	2₃₁ (laq)	632	4788	16128	20160	10080	2016	126
style="text-align:center;" \|2	{{CDD\|nodea\|3a\|nodea\|3a\|nodea\|3a\|branch\|3a\|nodea_1\|3a\|nodea}}	Rectified 2₃₁ (rolaq)	758	10332	47880	100800	90720	30240	2016
style="text-align:center;" \|3	{{CDD\|nodea\|3a\|nodea\|3a\|nodea\|3a\|branch_10\|3a\|nodea\|3a\|nodea}}	Rectified 1₃₂ (rolin)	758	12348	72072	191520	241920	120960	10080
style="text-align:center;" \|4	{{CDD\|nodea\|3a\|nodea\|3a\|nodea\|3a\|branch_01lr\|3a\|nodea\|3a\|nodea}}	1₃₂ (lin)	182	4284	23688	50400	40320	10080	576
style="text-align:center;" \|5	{{CDD\|nodea\|3a\|nodea\|3a\|nodea_1\|3a\|branch\|3a\|nodea\|3a\|nodea}}	Birectified 3₂₁ (branq)	758	12348	68040	161280	161280	60480	4032
style="text-align:center;" \|6	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea\|3a\|branch\|3a\|nodea\|3a\|nodea}}	Rectified 3₂₁ (ranq)	758	44352	70560	48384	11592	12096	756
style="text-align:center;" \|7	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea\|3a\|branch\|3a\|nodea\|3a\|nodea}}	3₂₁ (naq)	702	6048	12096	10080	4032	756	56
align=center \|8	{{CDD\|nodea\|3a\|nodea\|3a\|nodea\|3a\|branch\|3a\|nodea_1\|3a\|nodea_1}}	Truncated 2₃₁ (talq)	758	10332	47880	100800	90720	32256	4032
align=center \|9	{{CDD\|nodea\|3a\|nodea\|3a\|nodea\|3a\|branch_10\|3a\|nodea\|3a\|nodea_1}}	Cantellated 2₃₁ (sirlaq)						131040	20160
align=center \|10	{{CDD\|nodea\|3a\|nodea\|3a\|nodea\|3a\|branch_10\|3a\|nodea_1\|3a\|nodea}}	Bitruncated 2₃₁ (botlaq)							30240
align=center \|11	{{CDD\|nodea\|3a\|nodea\|3a\|nodea\|3a\|branch_01lr\|3a\|nodea\|3a\|nodea_1}}	small demified 2₃₁ (shilq)	2774	22428	78120	151200	131040	42336	4032
align=center \|12	{{CDD\|nodea\|3a\|nodea\|3a\|nodea\|3a\|branch_01lr\|3a\|nodea_1\|3a\|nodea}}	demirectified 2₃₁ (hirlaq)							12096
align=center \|13	{{CDD\|nodea\|3a\|nodea\|3a\|nodea\|3a\|branch_11\|3a\|nodea\|3a\|nodea}}	truncated 1₃₂ (tolin)							20160
align=center \|14	{{CDD\|nodea\|3a\|nodea\|3a\|nodea_1\|3a\|branch\|3a\|nodea\|3a\|nodea_1}}	small demiprismated 2₃₁ (shiplaq)							20160
align=center \|15	{{CDD\|nodea\|3a\|nodea\|3a\|nodea_1\|3a\|branch\|3a\|nodea_1\|3a\|nodea}}	birectified 1₃₂ (berlin)	758	22428	142632	403200	544320	302400	40320
align=center \|16	{{CDD\|nodea\|3a\|nodea\|3a\|nodea_1\|3a\|branch_10\|3a\|nodea\|3a\|nodea}}	tritruncated 3₂₁ (totanq)							40320
align=center \|17	{{CDD\|nodea\|3a\|nodea\|3a\|nodea_1\|3a\|branch_01lr\|3a\|nodea\|3a\|nodea}}	demibirectified 3₂₁ (hobranq)							20160
align=center \|18	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea\|3a\|branch\|3a\|nodea\|3a\|nodea_1}}	small cellated 2₃₁ (scalq)							7560
align=center \|19	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea\|3a\|branch\|3a\|nodea_1\|3a\|nodea}}	small biprismated 2₃₁ (sobpalq)							30240
align=center \|20	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea\|3a\|branch_10\|3a\|nodea\|3a\|nodea}}	small birhombated 3₂₁ (sabranq)							60480
align=center \|21	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea\|3a\|branch_01lr\|3a\|nodea\|3a\|nodea}}	demirectified 3₂₁ (harnaq)							12096
align=center \|22	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch\|3a\|nodea\|3a\|nodea}}	bitruncated 3₂₁ (botnaq)							12096
align=center \|23	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea\|3a\|branch\|3a\|nodea\|3a\|nodea_1}}	small terated 3₂₁ (stanq)							1512
align=center \|24	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea\|3a\|branch\|3a\|nodea_1\|3a\|nodea}}	small demicellated 3₂₁ (shocanq)							12096
align=center \|25	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea\|3a\|branch_10\|3a\|nodea\|3a\|nodea}}	small prismated 3₂₁ (spanq)							40320
align=center \|26	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea\|3a\|branch_01lr\|3a\|nodea\|3a\|nodea}}	small demified 3₂₁ (shanq)							4032
align=center \|27	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea_1\|3a\|branch\|3a\|nodea\|3a\|nodea}}	small rhombated 3₂₁ (sranq)							12096
align=center \|28	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea\|3a\|branch\|3a\|nodea\|3a\|nodea}}	Truncated 3₂₁ (tanq)	758	11592	48384	70560	44352	12852	1512
align=center \|29	{{CDD\|nodea\|3a\|nodea\|3a\|nodea\|3a\|branch_10\|3a\|nodea_1\|3a\|nodea_1}}	great rhombated 2₃₁ (girlaq)							60480
align=center \|30	{{CDD\|nodea\|3a\|nodea\|3a\|nodea\|3a\|branch_01lr\|3a\|nodea_1\|3a\|nodea_1}}	demitruncated 2₃₁ (hotlaq)							24192
align=center \|31	{{CDD\|nodea\|3a\|nodea\|3a\|nodea\|3a\|branch_11\|3a\|nodea\|3a\|nodea_1}}	small demirhombated 2₃₁ (sherlaq)							60480
align=center \|32	{{CDD\|nodea\|3a\|nodea\|3a\|nodea\|3a\|branch_11\|3a\|nodea_1\|3a\|nodea}}	demibitruncated 2₃₁ (hobtalq)							60480
align=center \|33	{{CDD\|nodea\|3a\|nodea\|3a\|nodea_1\|3a\|branch\|3a\|nodea_1\|3a\|nodea_1}}	demiprismated 2₃₁ (hiptalq)							80640
align=center \|34	{{CDD\|nodea\|3a\|nodea\|3a\|nodea_1\|3a\|branch_10\|3a\|nodea\|3a\|nodea_1}}	demiprismatorhombated 2₃₁ (hiprolaq)							120960
align=center \|35	{{CDD\|nodea\|3a\|nodea\|3a\|nodea_1\|3a\|branch_10\|3a\|nodea_1\|3a\|nodea}}	bitruncated 1₃₂ (batlin)							120960
align=center \|36	{{CDD\|nodea\|3a\|nodea\|3a\|nodea_1\|3a\|branch_01lr\|3a\|nodea\|3a\|nodea_1}}	small prismated 2₃₁ (spalq)							80640
align=center \|37	{{CDD\|nodea\|3a\|nodea\|3a\|nodea_1\|3a\|branch_01lr\|3a\|nodea_1\|3a\|nodea}}	small rhombated 1₃₂ (sirlin)							120960
align=center \|38	{{CDD\|nodea\|3a\|nodea\|3a\|nodea_1\|3a\|branch_11\|3a\|nodea\|3a\|nodea}}	tritruncated 2₃₁ (tatilq)							80640
align=center \|39	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea\|3a\|branch\|3a\|nodea_1\|3a\|nodea_1}}	cellitruncated 2₃₁ (catalaq)							60480
align=center \|40	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea\|3a\|branch_10\|3a\|nodea\|3a\|nodea_1}}	cellirhombated 2₃₁ (crilq)							362880
align=center \|41	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea\|3a\|branch_10\|3a\|nodea_1\|3a\|nodea}}	biprismatotruncated 2₃₁ (biptalq)							181440
align=center \|42	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea\|3a\|branch_01lr\|3a\|nodea\|3a\|nodea_1}}	small prismated 1₃₂ (seplin)							60480
align=center \|43	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea\|3a\|branch_01lr\|3a\|nodea_1\|3a\|nodea}}	small biprismated 3₂₁ (sabipnaq)							120960
align=center \|44	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea\|3a\|branch_11\|3a\|nodea\|3a\|nodea}}	small demibirhombated 3₂₁ (shobranq)							120960
align=center \|45	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch\|3a\|nodea\|3a\|nodea_1}}	cellidemiprismated 2₃₁ (chaplaq)							60480
align=center \|46	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch\|3a\|nodea_1\|3a\|nodea}}	demibiprismatotruncated 3₂₁ (hobpotanq)							120960
align=center \|47	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch_10\|3a\|nodea\|3a\|nodea}}	great birhombated 3₂₁ (gobranq)							120960
align=center \|48	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch_01lr\|3a\|nodea\|3a\|nodea}}	demibitruncated 3₂₁ (hobtanq)							60480
align=center \|49	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea\|3a\|branch\|3a\|nodea_1\|3a\|nodea_1}}	teritruncated 2₃₁ (totalq)							24192
align=center \|50	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea\|3a\|branch_10\|3a\|nodea\|3a\|nodea_1}}	terirhombated 2₃₁ (trilq)							120960
align=center \|51	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea\|3a\|branch_10\|3a\|nodea_1\|3a\|nodea}}	demicelliprismated 3₂₁ (hicpanq)							120960
align=center \|52	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea\|3a\|branch_01lr\|3a\|nodea\|3a\|nodea_1}}	small teridemified 2₃₁ (sethalq)							24192
align=center \|53	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea\|3a\|branch_01lr\|3a\|nodea_1\|3a\|nodea}}	small cellated 3₂₁ (scanq)							60480
align=center \|54	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea\|3a\|branch_11\|3a\|nodea\|3a\|nodea}}	demiprismated 3₂₁ (hipnaq)							80640
align=center \|55	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea_1\|3a\|branch\|3a\|nodea\|3a\|nodea_1}}	terirhombated 3₂₁ (tranq)							60480
align=center \|56	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea_1\|3a\|branch\|3a\|nodea_1\|3a\|nodea}}	demicellirhombated 3₂₁ (hocranq)							120960
align=center \|57	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea_1\|3a\|branch_10\|3a\|nodea\|3a\|nodea}}	prismatorhombated 3₂₁ (pranq)							120960
align=center \|58	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea_1\|3a\|branch_01lr\|3a\|nodea\|3a\|nodea}}	small demirhombated 3₂₁ (sharnaq)							60480
align=center \|59	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea\|3a\|branch\|3a\|nodea\|3a\|nodea_1}}	teritruncated 3₂₁ (tetanq)							15120
align=center \|60	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea\|3a\|branch\|3a\|nodea_1\|3a\|nodea}}	demicellitruncated 3₂₁ (hictanq)							60480
align=center \|61	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea\|3a\|branch_10\|3a\|nodea\|3a\|nodea}}	prismatotruncated 3₂₁ (potanq)							120960
align=center \|62	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea\|3a\|branch_01lr\|3a\|nodea\|3a\|nodea}}	demitruncated 3₂₁ (hotnaq)							24192
align=center \|63	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch\|3a\|nodea\|3a\|nodea}}	great rhombated 3₂₁ (granq)							24192
align=center \|64	{{CDD\|nodea\|3a\|nodea\|3a\|nodea\|3a\|branch_11\|3a\|nodea_1\|3a\|nodea_1}}	great demified 2₃₁ (gahlaq)							120960
align=center \|65	{{CDD\|nodea\|3a\|nodea\|3a\|nodea_1\|3a\|branch_10\|3a\|nodea_1\|3a\|nodea_1}}	great demiprismated 2₃₁ (gahplaq)							241920
align=center \|66	{{CDD\|nodea\|3a\|nodea\|3a\|nodea_1\|3a\|branch_01lr\|3a\|nodea_1\|3a\|nodea_1}}	prismatotruncated 2₃₁ (potlaq)							241920
align=center \|67	{{CDD\|nodea\|3a\|nodea\|3a\|nodea_1\|3a\|branch_11\|3a\|nodea\|3a\|nodea_1}}	prismatorhombated 2₃₁ (prolaq)							241920
align=center \|68	{{CDD\|nodea\|3a\|nodea\|3a\|nodea_1\|3a\|branch_11\|3a\|nodea_1\|3a\|nodea}}	great rhombated 1₃₂ (girlin)							241920
align=center \|69	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea\|3a\|branch_10\|3a\|nodea_1\|3a\|nodea_1}}	celligreatorhombated 2₃₁ (cagrilq)							362880
align=center \|70	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea\|3a\|branch_01lr\|3a\|nodea_1\|3a\|nodea_1}}	cellidemitruncated 2₃₁ (chotalq)							241920
align=center \|71	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea\|3a\|branch_11\|3a\|nodea\|3a\|nodea_1}}	prismatotruncated 1₃₂ (patlin)							362880
align=center \|72	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea\|3a\|branch_11\|3a\|nodea_1\|3a\|nodea}}	biprismatorhombated 3₂₁ (bipirnaq)							362880
align=center \|73	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch\|3a\|nodea_1\|3a\|nodea_1}}	tritruncated 1₃₂ (tatlin)							241920
align=center \|74	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch_10\|3a\|nodea\|3a\|nodea_1}}	cellidemiprismatorhombated 2₃₁ (chopralq)							362880
align=center \|75	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch_10\|3a\|nodea_1\|3a\|nodea}}	great demibiprismated 3₂₁ (ghobipnaq)							362880
align=center \|76	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch_01lr\|3a\|nodea\|3a\|nodea_1}}	celliprismated 2₃₁ (caplaq)							241920
align=center \|77	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch_01lr\|3a\|nodea_1\|3a\|nodea}}	biprismatotruncated 3₂₁ (boptanq)							362880
align=center \|78	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch_11\|3a\|nodea\|3a\|nodea}}	great trirhombated 2₃₁ (gatralaq)							241920
align=center \|79	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea\|3a\|branch_10\|3a\|nodea_1\|3a\|nodea_1}}	terigreatorhombated 2₃₁ (togrilq)							241920
align=center \|80	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea\|3a\|branch_01lr\|3a\|nodea_1\|3a\|nodea_1}}	teridemitruncated 2₃₁ (thotalq)							120960
align=center \|81	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea\|3a\|branch_11\|3a\|nodea\|3a\|nodea_1}}	teridemirhombated 2₃₁ (thorlaq)							241920
align=center \|82	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea\|3a\|branch_11\|3a\|nodea_1\|3a\|nodea}}	celliprismated 3₂₁ (capnaq)							241920
align=center \|83	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea_1\|3a\|branch\|3a\|nodea_1\|3a\|nodea_1}}	teridemiprismatotruncated 2₃₁ (thoptalq)							241920
align=center \|84	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea_1\|3a\|branch_10\|3a\|nodea\|3a\|nodea_1}}	teriprismatorhombated 3₂₁ (tapronaq)							362880
align=center \|85	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea_1\|3a\|branch_10\|3a\|nodea_1\|3a\|nodea}}	demicelliprismatorhombated 3₂₁ (hacpranq)							362880
align=center \|86	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea_1\|3a\|branch_01lr\|3a\|nodea\|3a\|nodea_1}}	teriprismated 2₃₁ (toplaq)							241920
align=center \|87	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea_1\|3a\|branch_01lr\|3a\|nodea_1\|3a\|nodea}}	cellirhombated 3₂₁ (cranq)							362880
align=center \|88	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea_1\|3a\|branch_11\|3a\|nodea\|3a\|nodea}}	demiprismatorhombated 3₂₁ (hapranq)							241920
align=center \|89	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea\|3a\|branch\|3a\|nodea_1\|3a\|nodea_1}}	tericellitruncated 2₃₁ (tectalq)							120960
align=center \|90	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea\|3a\|branch_10\|3a\|nodea\|3a\|nodea_1}}	teriprismatotruncated 3₂₁ (toptanq)							362880
align=center \|91	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea\|3a\|branch_10\|3a\|nodea_1\|3a\|nodea}}	demicelliprismatotruncated 3₂₁ (hecpotanq)							362880
align=center \|92	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea\|3a\|branch_01lr\|3a\|nodea\|3a\|nodea_1}}	teridemitruncated 3₂₁ (thotanq)							120960
align=center \|93	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea\|3a\|branch_01lr\|3a\|nodea_1\|3a\|nodea}}	cellitruncated 3₂₁ (catnaq)							241920
align=center \|94	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea\|3a\|branch_11\|3a\|nodea\|3a\|nodea}}	demiprismatotruncated 3₂₁ (hiptanq)							241920
align=center \|95	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch\|3a\|nodea\|3a\|nodea_1}}	terigreatorhombated 3₂₁ (tagranq)							120960
align=center \|96	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch\|3a\|nodea_1\|3a\|nodea}}	demicelligreatorhombated 3₂₁ (hicgarnq)							241920
align=center \|97	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch_10\|3a\|nodea\|3a\|nodea}}	great prismated 3₂₁ (gopanq)							241920
align=center \|98	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch_01lr\|3a\|nodea\|3a\|nodea}}	great demirhombated 3₂₁ (gahranq)							120960
align=center \|99	{{CDD\|nodea\|3a\|nodea\|3a\|nodea_1\|3a\|branch_11\|3a\|nodea_1\|3a\|nodea_1}}	great prismated 2₃₁ (gopalq)							483840
align=center \|100	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea\|3a\|branch_11\|3a\|nodea_1\|3a\|nodea_1}}	great cellidemified 2₃₁ (gechalq)							725760
align=center \|101	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch_10\|3a\|nodea_1\|3a\|nodea_1}}	great birhombated 1₃₂ (gebrolin)							725760
align=center \|102	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch_01lr\|3a\|nodea_1\|3a\|nodea_1}}	prismatorhombated 1₃₂ (prolin)							725760
align=center \|103	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch_11\|3a\|nodea\|3a\|nodea_1}}	celliprismatorhombated 2₃₁ (caprolaq)							725760
align=center \|104	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch_11\|3a\|nodea_1\|3a\|nodea}}	great biprismated 2₃₁ (gobpalq)							725760
align=center \|105	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea\|3a\|branch_11\|3a\|nodea_1\|3a\|nodea_1}}	tericelliprismated 3₂₁ (ticpanq)							483840
align=center \|106	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea_1\|3a\|branch_10\|3a\|nodea_1\|3a\|nodea_1}}	teridemigreatoprismated 2₃₁ (thegpalq)							725760
align=center \|107	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea_1\|3a\|branch_01lr\|3a\|nodea_1\|3a\|nodea_1}}	teriprismatotruncated 2₃₁ (teptalq)							725760
align=center \|108	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea_1\|3a\|branch_11\|3a\|nodea\|3a\|nodea_1}}	teriprismatorhombated 2₃₁ (topralq)							725760
align=center \|109	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea_1\|3a\|branch_11\|3a\|nodea_1\|3a\|nodea}}	cellipriemsatorhombated 3₂₁ (copranq)							725760
align=center \|110	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea\|3a\|branch_10\|3a\|nodea_1\|3a\|nodea_1}}	tericelligreatorhombated 2₃₁ (tecgrolaq)							725760
align=center \|111	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea\|3a\|branch_01lr\|3a\|nodea_1\|3a\|nodea_1}}	tericellitruncated 3₂₁ (tectanq)							483840
align=center \|112	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea\|3a\|branch_11\|3a\|nodea\|3a\|nodea_1}}	teridemiprismatotruncated 3₂₁ (thoptanq)							725760
align=center \|113	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea\|3a\|branch_11\|3a\|nodea_1\|3a\|nodea}}	celliprismatotruncated 3₂₁ (coptanq)							725760
align=center \|114	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch\|3a\|nodea_1\|3a\|nodea_1}}	teridemicelligreatorhombated 3₂₁ (thocgranq)							483840
align=center \|115	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch_10\|3a\|nodea\|3a\|nodea_1}}	terigreatoprismated 3₂₁ (tagpanq)							725760
align=center \|116	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch_10\|3a\|nodea_1\|3a\|nodea}}	great demicellated 3₂₁ (gahcnaq)							725760
align=center \|117	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch_01lr\|3a\|nodea\|3a\|nodea_1}}	tericelliprismated laq (tecpalq)							483840
align=center \|118	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch_01lr\|3a\|nodea_1\|3a\|nodea}}	celligreatorhombated 3₂₁ (cogranq)							725760
align=center \|119	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch_11\|3a\|nodea\|3a\|nodea}}	great demified 3₂₁ (gahnq)							483840
align=center \|120	{{CDD\|nodea\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch_11\|3a\|nodea_1\|3a\|nodea_1}}	great cellated 2₃₁ (gocalq)							1451520
align=center \|121	{{CDD\|nodea_1\|3a\|nodea\|3a\|nodea_1\|3a\|branch_11\|3a\|nodea_1\|3a\|nodea_1}}	terigreatoprismated 2₃₁ (tegpalq)							1451520
align=center \|122	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea\|3a\|branch_11\|3a\|nodea_1\|3a\|nodea_1}}	tericelliprismatotruncated 3₂₁ (tecpotniq)							1451520
align=center \|123	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch_10\|3a\|nodea_1\|3a\|nodea_1}}	tericellidemigreatoprismated 2₃₁ (techogaplaq)							1451520
align=center \|124	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch_01lr\|3a\|nodea_1\|3a\|nodea_1}}	tericelligreatorhombated 3₂₁ (tacgarnq)							1451520
align=center \|125	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch_11\|3a\|nodea\|3a\|nodea_1}}	tericelliprismatorhombated 2₃₁ (tecprolaq)							1451520
align=center \|126	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch_11\|3a\|nodea_1\|3a\|nodea}}	great cellated 3₂₁ (gocanq)							1451520
align=center \|127	{{CDD\|nodea_1\|3a\|nodea_1\|3a\|nodea_1\|3a\|branch_11\|3a\|nodea_1\|3a\|nodea_1}}	great terated 3₂₁ (gotanq)							2903040

Regular and uniform honeycombs

File:Coxeter diagram affine rank7 correspondence.png

There are five fundamental affine Coxeter groups and sixteen prismatic groups that generate regular and uniform tessellations in 6-space:

# !colspan=2\|Coxeter group !Coxeter diagram !Forms
class="wikitable"
align=center \|1	${\tilde{A}}_6$	[3^[7]]	{{CDD\|branch\|3ab\|nodes\|3ab\|nodes\|split2\|node}}	17
align=center \|2	${\tilde{C}}_6$	[4,3⁴,4]	{{CDD\|node\|4\|node\|3\|node\|3\|node\|3\|node\|3\|node\|4\|node}}	71
align=center \|3	${\tilde{B}}_6$	h[4,3⁴,4] [4,3³,3^1,1]	{{CDD\|nodes\|split2\|node\|3\|node\|3\|node\|3\|node\|4\|node}}	95 (32 new)
align=center \|4	${\tilde{D}}_6$	q[4,3⁴,4] [3^1,1,3²,3^1,1]	{{CDD\|nodes\|split2\|node\|3\|node\|3\|node\|split1\|nodes}}	41 (6 new)
align=center \|5	${\tilde{E}}_6$	[3^2,2,2]	{{CDD\|nodes\|3ab\|nodes\|split2\|node\|3\|node\|3\|node}}	39

Regular and uniform tessellations include:

${\tilde{A}}_6$ , 17 forms
Uniform 6-simplex honeycomb: {3^[7]} {{CDD|node_1|split1|nodes|3ab|nodes|3ab|nodes|3ab|branch}}
Uniform Cyclotruncated 6-simplex honeycomb: t_0,1{3^[7]} {{CDD|node|split1|nodes|3ab|nodes|3ab|nodes|3ab|branch_11}}
Uniform Omnitruncated 6-simplex honeycomb: t_{0,1,2,3,4,5,6,7}{3^[7]} {{CDD|node_1|split1|nodes_11|3ab|nodes_11|3ab|nodes_11|3ab|branch_11}}
${\tilde{C}}_6$ , [4,3⁴,4], 71 forms
Regular 6-cube honeycomb, represented by symbols {4,3⁴,4}, {{CDD|node_1|4|node|3|node|3|node|3|node|3|node|4|node}}
${\tilde{B}}_6$ , [3^1,1,3³,4], 95 forms, 64 shared with ${\tilde{C}}_6$ , 32 new
Uniform 6-demicube honeycomb, represented by symbols h{4,3⁴,4} = {3^1,1,3³,4}, {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node|4|node}} = {{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|4|node}}
${\tilde{D}}_6$ , [3^1,1,3²,3^1,1], 41 unique ringed permutations, most shared with ${\tilde{B}}_6$ and ${\tilde{C}}_6$ , and 6 are new. Coxeter calls the first one a quarter 6-cubic honeycomb.
{{CDD|nodes_10ru|split2|node|3|node|3|node|split1|nodes_10lu}} = {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node|4|node_h1}}
{{CDD|nodes_10ru|split2|node_1|3|node|3|node|split1|nodes_10lu}} = {{CDD|node_h1|4|node|3|node_1|3|node|3|node|3|node|4|node_h1}}
{{CDD|nodes_10ru|split2|node|3|node_1|3|node|split1|nodes_10lu}} = {{CDD|node_h1|4|node|3|node|3|node_1|3|node|3|node|4|node_h1}}
{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|split1|nodes_10lu}} = {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node|3|node|4|node_h1}}
{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|split1|nodes_10lu}} = {{CDD|node_h1|4|node|3|node_1|3|node|3|node_1|3|node|4|node_h1}}
{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|split1|nodes_10lu}} = {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node_1|3|node|4|node_h1}}
${\tilde{E}}_6$ : [3^2,2,2], 39 forms
Uniform 2₂₂ honeycomb: represented by symbols {3,3,3^2,2}, {{CDD|node_1|3|node||3|node|split1|nodes|3ab|nodes}}
Uniform t₄(2₂₂) honeycomb: 4r{3,3,3^2,2}, {{CDD|node|3|node||3|node|split1|nodes|3ab|nodes_11}}
Uniform 0₂₂₂ honeycomb: {3^2,2,2}, {{CDD|nodes|3ab|nodes|split2|node_1|3|node|3|node}}
Uniform t₂(0₂₂₂) honeycomb: 2r{3^2,2,2}, {{CDD|nodes_11|3ab|nodes|split2|node|3|node|3|node_1}}

# !colspan=2\|Coxeter group !Coxeter-Dynkin diagram
class=wikitable \|+ Prismatic groups
1	${\tilde{A}}_5$ x ${\tilde{I}}_1$	[3^[6],2,∞]	{{CDD\|node\|split1\|nodes\|3ab\|nodes\|split2\|node\|2\|node\|infin\|node}}
2	${\tilde{B}}_5$ x ${\tilde{I}}_1$	[4,3,3^1,1,2,∞]	{{CDD\|node\|4\|node\|3\|node\|3\|node\|3\|node\|4\|node\|2\|node\|infin\|node}}
3	${\tilde{C}}_5$ x ${\tilde{I}}_1$	[4,3³,4,2,∞]	{{CDD\|nodes\|split2\|node\|3\|node\|3\|node\|4\|node\|2\|node\|infin\|node}}
4	${\tilde{D}}_5$ x ${\tilde{I}}_1$	[3^1,1,3,3^1,1,2,∞]	{{CDD\|nodes\|split2\|node\|3\|node\|split1\|nodes\|2\|node\|infin\|node}}
5	${\tilde{A}}_4$ x ${\tilde{I}}_1$ x ${\tilde{I}}_1$	[3^[5],2,∞,2,∞,2,∞]	{{CDD\|branch\|3ab\|nodes\|split2\|node\|2\|node\|infin\|node\|2\|node\|infin\|node}}
6	${\tilde{B}}_4$ x ${\tilde{I}}_1$ x ${\tilde{I}}_1$	[4,3,3^1,1,2,∞,2,∞]	{{CDD\|nodes\|split2\|node\|3\|node\|4\|node\|2\|node\|infin\|node\|2\|node\|infin\|node}}
7	${\tilde{C}}_4$ x ${\tilde{I}}_1$ x ${\tilde{I}}_1$	[4,3,3,4,2,∞,2,∞]	{{CDD\|node\|4\|node\|3\|node\|3\|node\|4\|node\|2\|node\|infin\|node\|2\|node\|infin\|node}}
8	${\tilde{D}}_4$ x ${\tilde{I}}_1$ x ${\tilde{I}}_1$	[3^1,1,1,1,2,∞,2,∞]	{{CDD\|nodes\|split2\|node\|split1\|nodes\|2\|node\|infin\|node\|2\|node\|infin\|node}}
9	${\tilde{F}}_4$ x ${\tilde{I}}_1$ x ${\tilde{I}}_1$	[3,4,3,3,2,∞,2,∞]	{{CDD\|node\|3\|node\|4\|node\|3\|node\|3\|node\|2\|node\|infin\|node\|2\|node\|infin\|node}}
10	${\tilde{C}}_3$ x ${\tilde{I}}_1$ x ${\tilde{I}}_1$ x ${\tilde{I}}_1$	[4,3,4,2,∞,2,∞,2,∞]	{{CDD\|node\|4\|node\|3\|node\|4\|node\|2\|node\|infin\|node\|2\|node\|infin\|node\|2\|node\|infin\|node}}
11	${\tilde{B}}_3$ x ${\tilde{I}}_1$ x ${\tilde{I}}_1$ x ${\tilde{I}}_1$	[4,3^1,1,2,∞,2,∞,2,∞]	{{CDD\|nodes\|split2\|node\|4\|node\|2\|node\|infin\|node\|2\|node\|infin\|node\|2\|node\|infin\|node}}
12	${\tilde{A}}_3$ x ${\tilde{I}}_1$ x ${\tilde{I}}_1$ x ${\tilde{I}}_1$	[3^[4],2,∞,2,∞,2,∞]	{{CDD\|branch\|3ab\|branch\|2\|node\|infin\|node\|2\|node\|infin\|node\|2\|node\|infin\|node}}
13	${\tilde{C}}_2$ x ${\tilde{I}}_1$ x ${\tilde{I}}_1$ x ${\tilde{I}}_1$ x ${\tilde{I}}_1$	[4,4,2,∞,2,∞,2,∞,2,∞]	{{CDD\|node\|4\|node\|4\|node\|2\|node\|infin\|node\|2\|node\|infin\|node\|2\|node\|infin\|node\|2\|node\|infin\|node}}
14	${\tilde{H}}_2$ x ${\tilde{I}}_1$ x ${\tilde{I}}_1$ x ${\tilde{I}}_1$ x ${\tilde{I}}_1$	[6,3,2,∞,2,∞,2,∞,2,∞]	{{CDD\|node\|6\|node\|3\|node\|2\|node\|infin\|node\|2\|node\|infin\|node\|2\|node\|infin\|node\|2\|node\|infin\|node}}
15	${\tilde{A}}_2$ x ${\tilde{I}}_1$ x ${\tilde{I}}_1$ x ${\tilde{I}}_1$ x ${\tilde{I}}_1$	[3^[3],2,∞,2,∞,2,∞,2,∞]	{{CDD\|node\|split1\|branch\|2\|node\|infin\|node\|2\|node\|infin\|node\|2\|node\|infin\|node\|2\|node\|infin\|node}}
16	${\tilde{I}}_1$ x ${\tilde{I}}_1$ x ${\tilde{I}}_1$ x ${\tilde{I}}_1$ x ${\tilde{I}}_1$ x ${\tilde{I}}_1$	[∞,2,∞,2,∞,2,∞,2,∞]	{{CDD\|node\|infin\|node\|2\|node\|infin\|node\|2\|node\|infin\|node\|2\|node\|infin\|node\|2\|node\|infin\|node\|2\|node\|infin\|node}}

= Regular and uniform hyperbolic honeycombs =

There are no compact hyperbolic Coxeter groups of rank 7, groups that can generate honeycombs with all finite facets, and a finite vertex figure. However, there are 3 paracompact hyperbolic Coxeter groups of rank 7, each generating uniform honeycombs in 6-space as permutations of rings of the Coxeter diagrams.

class=wikitable

|align=right| ${\bar{P}}_6$ = [3,3^[6]]:
{{CDD|node|split1|nodes|3ab|nodes|split2|node|3|node}}

|align=right| ${\bar{Q}}_6$ = [3^1,1,3,3^2,1]:
{{CDD|nodea|3a|branch|3a|branch|3a|nodea|3a|nodea}}

|align=right| ${\bar{S}}_6$ = [4,3,3,3^2,1]:
{{CDD|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea|4a|nodea}}

Notes on the Wythoff construction for the uniform 7-polytopes

The reflective 7-dimensional uniform polytopes are constructed through a Wythoff construction process, and represented by a Coxeter-Dynkin diagram, where each node represents a mirror. An active mirror is represented by a ringed node. Each combination of active mirrors generates a unique uniform polytope. Uniform polytopes are named in relation to the regular polytopes in each family. Some families have two regular constructors and thus may be named in two equally valid ways.

Here are the primary operators available for constructing and naming the uniform 7-polytopes.

The prismatic forms and bifurcating graphs can use the same truncation indexing notation, but require an explicit numbering system on the nodes for clarity.

class="wikitable"
Operation !Extended Schläfli symbol !width=110\|Coxeter- Dynkin diagram !Description
Parent \|width=70\| t₀{p,q,r,s,t,u} \|{{CDD\|node_1\|p\|node\|q\|node\|r\|node\|s\|node\|t\|node\|u\|node}} \| Any regular 7-polytope
Rectified \| t₁{p,q,r,s,t,u} \|{{CDD\|node\|p\|node_1\|q\|node\|r\|node\|s\|node\|t\|node\|u\|node}} \|The edges are fully truncated into single points. The 7-polytope now has the combined faces of the parent and dual.
Birectified \| t₂{p,q,r,s,t,u} \|{{CDD\|node\|p\|node\|q\|node_1\|r\|node\|s\|node\|t\|node\|u\|node}} \|Birectification reduces cells to their duals.
Truncated \| t_0,1{p,q,r,s,t,u} \|{{CDD\|node_1\|p\|node_1\|q\|node\|r\|node\|s\|node\|t\|node\|u\|node}} \|Each original vertex is cut off, with a new face filling the gap. Truncation has a degree of freedom, which has one solution that creates a uniform truncated 7-polytope. The 7-polytope has its original faces doubled in sides, and contains the faces of the dual. 400px
Bitruncated \| t_1,2{p,q,r,s,t,u} \|{{CDD\|node\|p\|node_1\|q\|node_1\|r\|node\|s\|node\|t\|node\|u\|node}} \|Bitrunction transforms cells to their dual truncation.
Tritruncated \| t_2,3{p,q,r,s,t,u} \|{{CDD\|node\|p\|node\|q\|node_1\|r\|node_1\|s\|node\|t\|node\|u\|node}} \|Tritruncation transforms 4-faces to their dual truncation.
Cantellated \| t_0,2{p,q,r,s,t,u} \|{{CDD\|node_1\|p\|node\|q\|node_1\|r\|node\|s\|node\|t\|node\|u\|node}} \|In addition to vertex truncation, each original edge is beveled with new rectangular faces appearing in their place. A uniform cantellation is halfway between both the parent and dual forms. 400px
Bicantellated \| t_1,3{p,q,r,s,t,u} \|{{CDD\|node\|p\|node_1\|q\|node\|r\|node_1\|s\|node\|t\|node\|u\|node}} \|In addition to vertex truncation, each original edge is beveled with new rectangular faces appearing in their place. A uniform cantellation is halfway between both the parent and dual forms.
Runcinated \| t_0,3{p,q,r,s,t,u} \|{{CDD\|node_1\|p\|node\|q\|node\|r\|node_1\|s\|node\|t\|node\|u\|node}} \|Runcination reduces cells and creates new cells at the vertices and edges.
Biruncinated \| t_1,4{p,q,r,s,t,u} \|{{CDD\|node\|p\|node_1\|q\|node\|r\|node\|s\|node_1\|t\|node\|u\|node}} \|Runcination reduces cells and creates new cells at the vertices and edges.
Stericated \| t_0,4{p,q,r,s,t,u} \|{{CDD\|node_1\|p\|node\|q\|node\|r\|node\|s\|node_1\|t\|node\|u\|node}} \|Sterication reduces 4-faces and creates new 4-faces at the vertices, edges, and faces in the gaps.
Pentellated \| t_0,5{p,q,r,s,t,u} \|{{CDD\|node_1\|p\|node\|q\|node\|r\|node\|s\|node\|t\|node_1\|u\|node}} \|Pentellation reduces 5-faces and creates new 5-faces at the vertices, edges, faces, and cells in the gaps.
Hexicated \| t_0,6{p,q,r,s,t,u} \|{{CDD\|node_1\|p\|node\|q\|node\|r\|node\|s\|node\|t\|node\|u\|node_1}} \|Hexication reduces 6-faces and creates new 6-faces at the vertices, edges, faces, cells, and 4-faces in the gaps. (expansion operation for 7-polytopes)
Omnitruncated \| t_{0,1,2,3,4,5,6}{p,q,r,s,t,u} \|{{CDD\|node_1\|p\|node_1\|q\|node_1\|r\|node_1\|s\|node_1\|t\|node_1\|u\|node_1}} \|All six operators, truncation, cantellation, runcination, sterication, pentellation, and hexication are applied.

class="wikitable"

Operation

!Extended
Schläfli symbol

!width=110|Coxeter-
Dynkin
diagram

!Description

Parent

|width=70| t₀{p,q,r,s,t,u}

|{{CDD|node_1|p|node|q|node|r|node|s|node|t|node|u|node}}

| Any regular 7-polytope

Rectified

| t₁{p,q,r,s,t,u}

|{{CDD|node|p|node_1|q|node|r|node|s|node|t|node|u|node}}

|The edges are fully truncated into single points. The 7-polytope now has the combined faces of the parent and dual.

Birectified

| t₂{p,q,r,s,t,u}

|{{CDD|node|p|node|q|node_1|r|node|s|node|t|node|u|node}}

|Birectification reduces cells to their duals.

Truncated

| t_0,1{p,q,r,s,t,u}

|{{CDD|node_1|p|node_1|q|node|r|node|s|node|t|node|u|node}}

|Each original vertex is cut off, with a new face filling the gap. Truncation has a degree of freedom, which has one solution that creates a uniform truncated 7-polytope. The 7-polytope has its original faces doubled in sides, and contains the faces of the dual.
400px

Bitruncated

| t_1,2{p,q,r,s,t,u}

|{{CDD|node|p|node_1|q|node_1|r|node|s|node|t|node|u|node}}

|Bitrunction transforms cells to their dual truncation.

Tritruncated

| t_2,3{p,q,r,s,t,u}

|{{CDD|node|p|node|q|node_1|r|node_1|s|node|t|node|u|node}}

|Tritruncation transforms 4-faces to their dual truncation.

Cantellated

| t_0,2{p,q,r,s,t,u}

|{{CDD|node_1|p|node|q|node_1|r|node|s|node|t|node|u|node}}

|In addition to vertex truncation, each original edge is beveled with new rectangular faces appearing in their place. A uniform cantellation is halfway between both the parent and dual forms.
400px

Bicantellated

| t_1,3{p,q,r,s,t,u}

|{{CDD|node|p|node_1|q|node|r|node_1|s|node|t|node|u|node}}

|In addition to vertex truncation, each original edge is beveled with new rectangular faces appearing in their place. A uniform cantellation is halfway between both the parent and dual forms.

Runcinated

| t_0,3{p,q,r,s,t,u}

|{{CDD|node_1|p|node|q|node|r|node_1|s|node|t|node|u|node}}

|Runcination reduces cells and creates new cells at the vertices and edges.

Biruncinated

| t_1,4{p,q,r,s,t,u}

|{{CDD|node|p|node_1|q|node|r|node|s|node_1|t|node|u|node}}

|Runcination reduces cells and creates new cells at the vertices and edges.

Stericated

| t_0,4{p,q,r,s,t,u}

|{{CDD|node_1|p|node|q|node|r|node|s|node_1|t|node|u|node}}

|Sterication reduces 4-faces and creates new 4-faces at the vertices, edges, and faces in the gaps.

Pentellated

| t_0,5{p,q,r,s,t,u}

|{{CDD|node_1|p|node|q|node|r|node|s|node|t|node_1|u|node}}

|Pentellation reduces 5-faces and creates new 5-faces at the vertices, edges, faces, and cells in the gaps.

Hexicated

| t_0,6{p,q,r,s,t,u}

|{{CDD|node_1|p|node|q|node|r|node|s|node|t|node|u|node_1}}

|Hexication reduces 6-faces and creates new 6-faces at the vertices, edges, faces, cells, and 4-faces in the gaps. (expansion operation for 7-polytopes)

Omnitruncated

| t_{0,1,2,3,4,5,6}{p,q,r,s,t,u}

|{{CDD|node_1|p|node_1|q|node_1|r|node_1|s|node_1|t|node_1|u|node_1}}

|All six operators, truncation, cantellation, runcination, sterication, pentellation, and hexication are applied.

References

T. Gosset: On the Regular and Semi-Regular Figures in Space of n Dimensions, Messenger of Mathematics, Macmillan, 1900
A. Boole Stott: Geometrical deduction of semiregular from regular polytopes and space fillings, Verhandelingen of the Koninklijke academy van Wetenschappen width unit Amsterdam, Eerste Sectie 11,1, Amsterdam, 1910
H.S.M. Coxeter:
H.S.M. Coxeter, M.S. Longuet-Higgins und J.C.P. Miller: Uniform Polyhedra, Philosophical Transactions of the Royal Society of London, Londne, 1954
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, {{isbn|978-0-471-01003-6}} http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
(Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. Dissertation, University of Toronto, 1966
{{KlitzingPolytopes|polyexa.htm|7D|uniform polytopes (polyexa)}}

External links

[http://www.steelpillow.com/polyhedra/ditela.html Polytope names]
[http://www.polytope.net/hedrondude/topes.htm Polytopes of Various Dimensions]
[http://tetraspace.alkaline.org/glossary.htm Multi-dimensional Glossary]

Category:7-polytopes

uniform 7-polytope

Regular 7-polytopes

Characteristics

Uniform 7-polytopes by fundamental Coxeter groups

The A<sub>7</sub> family

The B<sub>7</sub> family

The D<sub>7</sub> family

The E<sub>7</sub> family

Regular and uniform honeycombs

= Regular and uniform hyperbolic honeycombs =

Notes on the Wythoff construction for the uniform 7-polytopes

References

External links