Runcinated 5-orthoplexes#Runcicantitruncated 5-orthoplex

• Runcinated pentacross
• Small prismated triacontiditeron (Acronym: spat) (Jonathan Bowers)Klitzing, (x3o3o3x4o - spat)

The vertices of the can be made in 5-space, as permutations and sign combinations of:

: (0,1,1,1,2)

{{5-cube Coxeter plane graphs|t14|150}}

• Runcitruncated pentacross
• Prismatotruncated triacontiditeron (Acronym: pattit) (Jonathan Bowers)Klitzing, (x3x3o3x4o - pattit)

Cartesian coordinates for the vertices of a runcitruncated 5-orthoplex, centered at the origin, are all 80 vertices are sign (4) and coordinate (20) permutations of

: (±3,±2,±1,±1,0)

{{5-cube Coxeter plane graphs|t134|150}}

• Runcicantellated pentacross
• Prismatorhombated triacontiditeron (Acronym: pirt) (Jonathan Bowers)Klitzing, (x3o3x3x4o - pirt)

The vertices of the runcicantellated 5-orthoplex can be made in 5-space, as permutations and sign combinations of:

: (0,1,2,2,3)

{{5-cube Coxeter plane graphs|t124|150}}

• Runcicantitruncated pentacross
• Great prismated triacontiditeron (gippit) (Jonathan Bowers)Klitzing, (x3x3x3x4o - gippit)

The Cartesian coordinates of the vertices of a runcicantitruncated 5-orthoplex having an edge length of {{radic|2}} are given by all permutations of coordinates and sign of:

:$\backslash left(0,\; 1,\; 2,\; 3,\; 4\backslash right)$

{{5-cube Coxeter plane graphs|t1234|150}}

The snub 5-demicube defined as an alternation of the omnitruncated 5-demicube is not uniform, but it can be given Coxeter diagram {{CDD|nodes_hh|split2|node_h|3|node_h|3|node_h}} or {{CDD|node|4|node_h|3|node_h|3|node_h|3|node_h}} and symmetry [3^2,1,1]⁺ or [4,(3,3,3)⁺], and constructed from 10 snub 24-cells, 32 snub 5-cells, 40 snub tetrahedral antiprisms, 80 2-3 duoantiprisms, and 960 irregular 5-cells filling the gaps at the deleted vertices.

This polytope is one of 31 uniform 5-polytopes generated from the regular 5-cube or 5-orthoplex.

{{Penteract family}}

{{reflist}}

• H.S.M. Coxeter:
• 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 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]
• Norman Johnson Uniform Polytopes, Manuscript (1991)
• N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D.
• {{KlitzingPolytopes|polytera.htm|5D|uniform polytopes (polytera)}} x3o3o3x4o - spat, x3x3o3x4o - pattit, x3o3x3x4o - pirt, x3x3x3x4o - gippit

• {{PolyCell | urlname = glossary.html#simplex| title = Glossary for hyperspace}}
• [http://www.polytope.net/hedrondude/topes.htm Polytopes of Various Dimensions], Jonathan Bowers
• [http://www.polytope.net/hedrondude/truncates5.htm Runcinated uniform polytera] (spid), Jonathan Bowers
• [http://tetraspace.alkaline.org/glossary.htm Multi-dimensional Glossary]

{{Polytopes}}

Category:5-polytopes