1 32 polytope

{{Short description|Uniform polytope}}

{{DISPLAYTITLE:1 32 polytope}}

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|colspan=2|120px
321
{{CDD|nodea_1|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea}}

|colspan=2|120px
231
{{CDD|nodea|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea_1}}

|colspan=2|120px
132
{{CDD|nodea|3a|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea}}

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|colspan=3|150px
Rectified 321
{{CDD|nodea|3a|nodea_1|3a|nodea|3a|branch|3a|nodea|3a|nodea}}

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Birectified 321
{{CDD|nodea|3a|nodea|3a|nodea_1|3a|branch|3a|nodea|3a|nodea}}

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|colspan=3|150px
Rectified 231
{{CDD|nodea|3a|nodea|3a|nodea|3a|branch|3a|nodea_1|3a|nodea}}

|colspan=3 valign=center|150px
Rectified 132
{{CDD|nodea|3a|nodea|3a|nodea|3a|branch_10|3a|nodea|3a|nodea}}

valign="top"

! colspan="6" |Orthogonal projections in E7 Coxeter plane

In 7-dimensional geometry, 132 is a uniform polytope, constructed from the E7 group.

Its Coxeter symbol is 132, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of one of the 1-node sequences.

The rectified 132 is constructed by points at the mid-edges of the 132.

These polytopes are part of a family of 127 (27-1) convex uniform polytopes in 7-dimensions, made of uniform polytope facets and vertex figures, defined by all permutations of rings in this Coxeter-Dynkin diagram: {{CDD|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea}}.

{{clear}}

1<sub>32</sub> polytope

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!bgcolor=#e7dcc3 colspan=2|132

bgcolor=#e7dcc3|TypeUniform 7-polytope
bgcolor=#e7dcc3|Family1k2 polytope
bgcolor=#e7dcc3|Schläfli symbol{3,33,2}
bgcolor=#e7dcc3|Coxeter symbol132
bgcolor=#e7dcc3|Coxeter diagram{{CDD|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea|3a|nodea}}
bgcolor=#e7dcc3|6-faces182:
56 122 30px
126 131 30px
bgcolor=#e7dcc3|5-faces4284:
756 121 25px
1512 121 25px
2016 {34} 25px
bgcolor=#e7dcc3|4-faces23688:
4032 {33} 25px
7560 111 25px
12096 {33} 25px
bgcolor=#e7dcc3|Cells50400:
20160 {32} 25px
30240 {32} 25px
8

|bgcolor=#e7dcc3|Faces

40320 {3}25px
bgcolor=#e7dcc3|Edges10080
bgcolor=#e7dcc3|Vertices576
bgcolor=#e7dcc3|Vertex figuret2{35} 25px
bgcolor=#e7dcc3|Petrie polygonOctadecagon
bgcolor=#e7dcc3|Coxeter groupE7, [33,2,1], order 2903040
bgcolor=#e7dcc3|Propertiesconvex

This polytope can tessellate 7-dimensional space, with symbol 133, and Coxeter-Dynkin diagram, {{CDD|nodea|3a|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea|3a|nodea}}. It is the Voronoi cell of the dual E7* lattice.[http://home.digital.net/~pervin/publications/vermont.html The Voronoi Cells of the E6* and E7* Lattices] {{Webarchive|url=https://web.archive.org/web/20160130193811/http://home.digital.net/~pervin/publications/vermont.html |date=2016-01-30 }}, Edward Pervin

= Alternate names =

  • Emanuel Lodewijk Elte named it V576 (for its 576 vertices) in his 1912 listing of semiregular polytopes.Elte, 1912
  • Coxeter called it 132 for its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 1-node branch.
  • Pentacontahexa-hecatonicosihexa-exon (Acronym: lin) - 56-126 facetted polyexon (Jonathan Bowers)Klitzing, (o3o3o3x *c3o3o3o - lin)

= Images =

class=wikitable width=600

|+ Coxeter plane projections

E7

!E6 / F4

!B7 / A6

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|200px
[18]

|200px
[12]

|200px
[7x2]

A5

!D7 / B6

!D6 / B5

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|200px
[6]

|200px
[12/2]

|200px
[10]

D5 / B4 / A4

!D4 / B3 / A2 / G2

!D3 / B2 / A3

valign=top align=center

|200px
[8]

|200px
[6]

|200px
[4]

= Construction =

It is created by a Wythoff construction upon a set of 7 hyperplane mirrors in 7-dimensional space.

The facet information can be extracted from its Coxeter-Dynkin diagram, {{CDD|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea|3a|nodea}}

Removing the node on the end of the 2-length branch leaves the 6-demicube, 131, {{CDD|nodea|3a|branch_01lr|3a|nodea|3a|nodea|3a|nodea}}

Removing the node on the end of the 3-length branch leaves the 122, {{CDD|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea}}

The vertex figure is determined by removing the ringed node and ringing the neighboring node. This makes the birectified 6-simplex, 032, {{CDD|nodea|3a|nodea|3a|nodea_1|3a|nodea|3a|nodea|3a|nodea}}

Seen in a configuration matrix, the element counts can be derived by mirror removal and ratios of Coxeter group orders.Coxeter, Regular Polytopes, 11.8 Gossett figures in six, seven, and eight dimensions, p. 202-203

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!E7

{{CDD|nodea|3a|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea}}k-facefkf0f1f2colspan=2|f3colspan=3|f4colspan=3|f5colspan=2|f6k-figuresnotes
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|A6

width=65|{{CDD|nodea|3a|nodea|3a|nodea|3a|nodes_0x|3a|nodea|3a|nodea}}( )

!f0

|BGCOLOR="#ffe0ff"|576

3521014021035105105214221772r{3,3,3,3,3}E7/A6 = 72*8!/7! = 576
align=right

|A3A2A1

{{CDD|nodea|3a|nodea|3a|nodea|2|nodes_x1|2|nodea|3a|nodea}}{ }

!f1

2BGCOLOR="#ffe0e0"|1008012121841212612343{3,3}x{3}E7/A3A2A1 = 72*8!/4!/3!/2 = 10080
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|A2A2A1

{{CDD|nodea|3a|nodea|2|nodea_x|2|branch_01|2|nodea_x|2|nodea}}{3}

!f2

33BGCOLOR="#ffffe0"|403202316336132{ }∨{3}E7/A2A2A1 = 72*8!/3!/3!/2 = 40320
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|A3A2

{{CDD|nodea|3a|nodea|2|nodea_x|2|branch_01r|3a|nodea|2|nodea_x}}rowspan=2|{3,3}

!rowspan=2|f3

464BGCOLOR="#e0ffe0"|20160BGCOLOR="#e0ffe0"|*13033031{3}∨( )E7/A3A2 = 72*8!/4!/3! = 20160
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|A3A1A1

{{CDD|nodea|2|nodea_x|2|nodea|3a|branch_01l|2|nodea_x|2|nodea}}464BGCOLOR="#e0ffe0"|*BGCOLOR="#e0ffe0"|3024002214122Phyllic disphenoidE7/A3A1A1 = 72*8!/4!/2/2 = 30240
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|A4A2

{{CDD|nodea|3a|nodea|2|nodea_x|2|branch_01r|3a|nodea|3a|nodea}}{3,3,3}

!rowspan=3|f4

5101050BGCOLOR="#e0ffff"|4032BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|*30030{3}E7/A4A2 = 72*8!/5!/3! = 4032
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|D4A1

{{CDD|nodea|2|nodea_x|2|nodea|3a|branch_01lr|3a|nodea|2|nodea_x}}{3,3,4}8243288BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|7560BGCOLOR="#e0ffff"|*12021rowspan=2|{ }∨( )E7/D4A1 = 72*8!/8/4!/2 = 7560
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|A4A1

{{CDD|nodea_x|2|nodea|3a|nodea|3a|branch_01l|2|nodea_x|2|nodea}}{3,3,3}5101005BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|1209602112E7/A4A1 = 72*8!/5!/2 = 12096
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|D5A1

{{CDD|nodea|2|nodea_x|2|nodea|3a|branch_01lr|3a|nodea|3a|nodea}}rowspan=2|h{4,3,3,3}

!rowspan=3|f5

1680160804016100BGCOLOR="#e0e0ff"|756BGCOLOR="#e0e0ff"|*BGCOLOR="#e0e0ff"|*20rowspan=3|{ }E7/D5A1 = 72*8!/16/5!/2 = 756
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|D5

{{CDD|nodea_x|2|nodea|3a|nodea|3a|branch_01lr|3a|nodea|2|nodea_x}}1680160408001016BGCOLOR="#e0e0ff"|*BGCOLOR="#e0e0ff"|1512BGCOLOR="#e0e0ff"|*11E7/D5 = 72*8!/16/5! = 1512
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|A5A1

{{CDD|nodea|3a|nodea|3a|nodea|3a|branch_01l|2|nodea_x|2|nodea}}{3,3,3,3,3} 61520015006BGCOLOR="#e0e0ff"|*BGCOLOR="#e0e0ff"|*BGCOLOR="#e0e0ff"|201602E7/A5A1 = 72*8!/6!/2 = 2016
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|E6

{{CDD|nodea_x|2|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea}}{3,32,2}

!rowspan=2|f6

7272021601080108021627021627270BGCOLOR="#ffe0ff"|56BGCOLOR="#ffe0ff"|*rowspan=2|( )E7/E6 = 72*8!/72/6! = 56
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|D6

{{CDD|nodea|3a|nodea|3a|nodea|3a|branch_01lr|3a|nodea|2|nodea_x}}h{4,3,3,3,3} 3224064016048006019201232BGCOLOR="#ffe0ff"|*BGCOLOR="#ffe0ff"|126E7/D6 = 72*8!/32/6! = 126

= Related polytopes and honeycombs =

The 132 is third in a dimensional series of uniform polytopes and honeycombs, expressed by Coxeter as 13k series. The next figure is the Euclidean honeycomb 133 and the final is a noncompact hyperbolic honeycomb, 134.

{{1 3k polytopes}}

{{1 k2 polytopes}}

Rectified 1<sub>32</sub> polytope

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!bgcolor=#e7dcc3 colspan=2|Rectified 132

bgcolor=#e7dcc3|TypeUniform 7-polytope
bgcolor=#e7dcc3|Schläfli symbolt1{3,33,2}
bgcolor=#e7dcc3|Coxeter symbol0321
bgcolor=#e7dcc3|Coxeter-Dynkin diagram{{CDD|nodea|3a|nodea|3a|branch_10|3a|nodea|3a|nodea|3a|nodea}}
bgcolor=#e7dcc3|6-faces758
bgcolor=#e7dcc3|5-faces12348
bgcolor=#e7dcc3|4-faces72072
bgcolor=#e7dcc3|Cells191520
bgcolor=#e7dcc3|Faces241920
bgcolor=#e7dcc3|Edges120960
bgcolor=#e7dcc3|Vertices10080
bgcolor=#e7dcc3|Vertex figure{3,3}×{3}×{}
bgcolor=#e7dcc3|Coxeter groupE7, [33,2,1], order 2903040
bgcolor=#e7dcc3|Propertiesconvex

The rectified 132 (also called 0321) is a rectification of the 132 polytope, creating new vertices on the center of edge of the 132. Its vertex figure is a duoprism prism, the product of a regular tetrahedra and triangle, doubled into a prism: {3,3}×{3}×{}.

= Alternate names =

  • Rectified pentacontahexa-hecatonicosihexa-exon for rectified 56-126 facetted polyexon (Acronym: rolin) (Jonathan Bowers)Klitzing, (o3o3x3o *c3o3o3o - rolin)

= Construction =

It is created by a Wythoff construction upon a set of 7 hyperplane mirrors in 7-dimensional space. These mirrors are represented by its Coxeter-Dynkin diagram, {{CDD|nodea|3a|nodea|3a|branch_10|3a|nodea|3a|nodea|3a|nodea}}, and the ring represents the position of the active mirror(s).

Removing the node on the end of the 3-length branch leaves the rectified 122 polytope, {{CDD|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea}}

Removing the node on the end of the 2-length branch leaves the demihexeract, 131, {{CDD|nodea|3a|branch_01lr|3a|nodea|3a|nodea|3a|nodea}}

Removing the node on the end of the 1-length branch leaves the birectified 6-simplex, {{CDD|nodea|3a|nodea|3a|nodea_1|3a|nodea|3a|nodea|3a|nodea}}

The vertex figure is determined by removing the ringed node and ringing the neighboring node. This makes the tetrahedron-triangle duoprism prism, {3,3}×{3}×{}, {{CDD|nodea|3a|nodea_1|2|nodea_1|2|nodea_1|3a|nodea|3a|nodea}}

Seen in a configuration matrix, the element counts can be derived by mirror removal and ratios of Coxeter group orders.

class=wikitable width=1700

!E7

{{CDD|nodea|3a|nodea|3a|nodea|3a|branch_10|3a|nodea|3a|nodea}}k-facefkf0f1colspan=3|f2colspan=5|f3colspan=6|f4colspan=5|f5colspan=3|f6k-figuresnotes
align=right

|A3A2A1

{{CDD|nodea|3a|nodea|3a|nodea|2|nodes_x0|2|nodea|3a|nodea}}( )

!f0

|BGCOLOR="#ffe0ff"|10080

242412368123618244121824126681263423{3,3}x{3}x{ }E7/A3A2A1 = 72*8!/4!/3!/2 = 10080
align=right

|A2A1A1

{{CDD|nodea|3a|nodea|2|nodea_x|2|nodes_1x|2|nodea_x|2|nodea}}{ }

!f1

2BGCOLOR="#ffe0e0"|1209602131263313663133621312( )v{3}v{ }E7/A2A1A1 = 72*8!/3!/2/2 = 120960
align=right

|A2A2

{{CDD|nodea|3a|nodea|2|nodea_x|2|nodes_1x|3a|nodea|2|nodea_x}}rowspan=3|01

!rowspan=3|f2

33BGCOLOR="#ffffe0"|80640BGCOLOR="#ffffe0"|*BGCOLOR="#ffffe0"|*1130013330033310311{3}v( )v( )E7/A2A2 = 72*8!/3!/3! = 80640
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|A2A2A1

{{CDD|nodea|3a|nodea|2|nodea_x|2|branch_10|2|nodea_x|2|nodea}}33BGCOLOR="#ffffe0"|*BGCOLOR="#ffffe0"|40320BGCOLOR="#ffffe0"|*0203010603030601302{3}v{ }E7/A2A2A1 = 72*8!/3!/3!/2 = 40320
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|A2A1A1

{{CDD|nodea|2|nodea_x|2|nodea|3a|nodes_1x|2|nodea_x|2|nodea}}33BGCOLOR="#ffffe0"|*BGCOLOR="#ffffe0"|*BGCOLOR="#ffffe0"|1209600021201242112421212{ }v{ }v( )E7/A2A1A1 = 72*8!/3!/2/2 = 120960
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|rowspan=2|A3A2

{{CDD|nodea|3a|nodea|2|nodea_x|2|nodes_1x|3a|nodea|3a|nodea}}02

!rowspan=5|f3

46400BGCOLOR="#e0ffe0"|20160BGCOLOR="#e0ffe0"|*BGCOLOR="#e0ffe0"|*BGCOLOR="#e0ffe0"|*BGCOLOR="#e0ffe0"|*13000033000310rowspan=2|{3}v( )rowspan=2|E7/A3A2 = 72*8!/4!/3! = 20160
align=right

|{{CDD|nodea|3a|nodea|2|nodea_x|2|branch_10|3a|nodea|2|nodea_x}}

rowspan=3| 011612440BGCOLOR="#e0ffe0"|*BGCOLOR="#e0ffe0"|20160BGCOLOR="#e0ffe0"|*BGCOLOR="#e0ffe0"|*BGCOLOR="#e0ffe0"|*10300030300301
align=right

|A3A1

{{CDD|nodea|2|nodea_x|2|nodea|3a|nodes_1x|3a|nodea|2|nodea_x}}612404BGCOLOR="#e0ffe0"|*BGCOLOR="#e0ffe0"|*BGCOLOR="#e0ffe0"|60480BGCOLOR="#e0ffe0"|*BGCOLOR="#e0ffe0"|*01120012210211SphenoidE7/A3A1 = 72*8!/4!/2 = 60480
align=right

|A3A1A1

{{CDD|nodea|2|nodea_x|2|nodea|3a|branch_10|2|nodea_x|2|nodea}}612044BGCOLOR="#e0ffe0"|*BGCOLOR="#e0ffe0"|*BGCOLOR="#e0ffe0"|*BGCOLOR="#e0ffe0"|30240BGCOLOR="#e0ffe0"|*00202010401202{ }v{ }E7/A3A1A1 = 72*8!/4!/2/2 = 30240
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|A3A1

{{CDD|nodea_x|2|nodea|3a|nodea|3a|nodes_1x|2|nodea_x|2|nodea}}0246004BGCOLOR="#e0ffe0"|*BGCOLOR="#e0ffe0"|*BGCOLOR="#e0ffe0"|*BGCOLOR="#e0ffe0"|*BGCOLOR="#e0ffe0"|6048000021101221112SphenoidE7/A3A1 = 72*8!/4!/2 = 60480
align=right

|A4A2

{{CDD|nodea|3a|nodea|2|nodea_x|2|branch_10|3a|nodea|3a|nodea}}rowspan=2|021

!rowspan=6|f4

10302010055000BGCOLOR="#e0ffff"|4032BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|*30000300{3}E7/A4A2 = 72*8!/5!/3! = 4032
align=right

|A4A1

{{CDD|nodea|2|nodea_x|2|nodea|3a|nodes_1x|3a|nodea|3a|nodea}}10302001050500BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|12096BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|*12000210rowspan=2|{ }v()E7/A4A1 = 72*8!/5!/2 = 12096
align=right

|D4A1

{{CDD|nodea|2|nodea_x|2|nodea|3a|branch_10|3a|nodea|2|nodea_x}}0111249632323208880BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|7560BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|*10200201E7/D4A1 = 72*8!/8/4!/2 = 7560
align=right

|A4

{{CDD|nodea_x|2|nodea|3a|nodea|3a|nodes_1x|3a|nodea|2|nodea_x}}rowspan=2|02110301002000505BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|24192BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|*01110111( )v( )v( )E7/A4 = 72*8!/5! = 34192
align=right

|rowspan=2|A4A1

{{CDD|nodea_x|2|nodea|3a|nodea|3a|branch_10|2|nodea_x|2|nodea}}10300102000055BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|12096BGCOLOR="#e0ffff"|*00201102rowspan=2|{ }v()rowspan=2|E7/A4A1 = 72*8!/5!/2 = 12096
align=right

|{{CDD|nodea|3a|nodea|3a|nodea|3a|nodes_1x|2|nodea_x|2|nodea}}

03510001000005BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|*BGCOLOR="#e0ffff"|1209600021012
align=right

|D5A1

{{CDD|nodea|2|nodea_x|2|nodea|3a|branch_10|3a|nodea|3a|nodea}}0211

!rowspan=5|f5

80480320160160808080400161610000BGCOLOR="#e0e0ff"|756BGCOLOR="#e0e0ff"|*BGCOLOR="#e0e0ff"|*BGCOLOR="#e0e0ff"|*BGCOLOR="#e0e0ff"|*200rowspan=5|{ }E7/D5A1 = 72*8!/16/5!/2 = 756
align=right

|A5

{{CDD|nodea_x|2|nodea|3a|nodea|3a|nodes_1x|3a|nodea|3a|nodea}}02220906006015030015060600BGCOLOR="#e0e0ff"|*BGCOLOR="#e0e0ff"|4032BGCOLOR="#e0e0ff"|*BGCOLOR="#e0e0ff"|*BGCOLOR="#e0e0ff"|*110E7/A5 = 72*8!/6! = 4032
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|D5

{{CDD|nodea_x|2|nodea|3a|nodea|3a|branch_10|3a|nodea|2|nodea_x}}021180480160160320040808080001016160BGCOLOR="#e0e0ff"|*BGCOLOR="#e0e0ff"|*BGCOLOR="#e0e0ff"|1512BGCOLOR="#e0e0ff"|*BGCOLOR="#e0e0ff"|*101E7/D5 = 72*8!/16/5! = 1512
align=right

|A5

{{CDD|nodea|3a|nodea|3a|nodea|3a|nodes_1x|3a|nodea|2|nodea_x}}rowspan=2|0311560200600015030000606BGCOLOR="#e0e0ff"|*BGCOLOR="#e0e0ff"|*BGCOLOR="#e0e0ff"|*BGCOLOR="#e0e0ff"|4032BGCOLOR="#e0e0ff"|*011E7/A5 = 72*8!/6! = 4032
align=right

|A5A1

{{CDD|nodea|3a|nodea|3a|nodea|3a|branch_10|2|nodea_x|2|nodea}}1560020600001530000066BGCOLOR="#e0e0ff"|*BGCOLOR="#e0e0ff"|*BGCOLOR="#e0e0ff"|*BGCOLOR="#e0e0ff"|*BGCOLOR="#e0e0ff"|2016002E7/A5A1 = 72*8!/6!/2 = 2016
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|E6

{{CDD|nodea_x|2|nodea|3a|nodea|3a|branch_10|3a|nodea|3a|nodea}}0221

!rowspan=3|f6

720648043202160432010801080216010801080216432270432216027722700BGCOLOR="#ffe0ff"|56BGCOLOR="#ffe0ff"|*BGCOLOR="#ffe0ff"|*rowspan=3|( )E7/E6 = 72*8!/72/6! = 56
align=right

|A6

{{CDD|nodea|3a|nodea|3a|nodea|3a|nodes_1x|3a|nodea|3a|nodea}}032352101400210350105010502104202107070BGCOLOR="#ffe0ff"|*BGCOLOR="#ffe0ff"|576BGCOLOR="#ffe0ff"|*E7/A6 = 72*8!/7! = 576
align=right

|D6

{{CDD|nodea|3a|nodea|3a|nodea|3a|branch_10|3a|nodea|2|nodea_x}}0311240192064064019200160480480960006019219219200123232BGCOLOR="#ffe0ff"|*BGCOLOR="#ffe0ff"|*BGCOLOR="#ffe0ff"|126E7/D6 = 72*8!/32/6! = 126

= Images =

class=wikitable width=600

|+ Coxeter plane projections

E7

!E6 / F4

!B7 / A6

valign=top align=center

|200px
[18]

|200px
[12]

|200px
[14]

A5

!D7 / B6

!D6 / B5

valign=top align=center

|200px
[6]

|200px
[12/2]

|200px
[10]

D5 / B4 / A4

!D4 / B3 / A2 / G2

!D3 / B2 / A3

valign=top align=center

|200px
[8]

|200px
[6]

|200px
[4]

See also

Notes

{{reflist}}

References

  • {{citation | last = Elte | first = E. L. | title = The Semiregular Polytopes of the Hyperspaces | publisher = University of Groningen | location = Groningen | year = 1912}}
  • 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, [https://www.wiley.com/en-us/Kaleidoscopes-p-9780471010036 wiley.com], {{isbn|978-0-471-01003-6}}
  • (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
  • {{KlitzingPolytopes|polyexa.htm|7D uniform polytopes (polyexa)}} o3o3o3x *c3o3o3o - lin, o3o3x3o *c3o3o3o - rolin

{{Polytopes}}

Category:7-polytopes