Runcinated 5-cubes#Runcinated 5-cube

• Small prismated penteract (Acronym: span) (Jonathan Bowers)

The Cartesian coordinates of the vertices of a runcinated 5-cube having edge length 2 are all permutations of:

:$\backslash left(\backslash pm1,\backslash \; \backslash pm1,\backslash \; \backslash pm1,\backslash \; \backslash pm(1+\backslash sqrt\{2\}),\backslash \; \backslash pm(1+\backslash sqrt\{2\})\backslash right)$

{{5-cube Coxeter plane graphs|t03|150}}

• Runcitruncated penteract
• Prismatotruncated penteract (Acronym: pattin) (Jonathan Bowers)

The Cartesian coordinates of the vertices of a runcitruncated 5-cube having edge length 2 are all permutations of:

:$\backslash left(\backslash pm1,\backslash \; \backslash pm(1+\backslash sqrt\{2\}),\backslash \; \backslash pm(1+\backslash sqrt\{2\}),\backslash \; \backslash pm(1+2\backslash sqrt\{2\}),\backslash \; \backslash pm(1+2\backslash sqrt\{2\})\backslash right)$

{{5-cube Coxeter plane graphs|t013|150}}

• Runcicantellated penteract
• Prismatorhombated penteract (Acronym: prin) (Jonathan Bowers)

The Cartesian coordinates of the vertices of a runcicantellated 5-cube having edge length 2 are all permutations of:

:$\backslash left(\backslash pm1,\backslash \; \backslash pm1,\backslash \; \backslash pm(1+\backslash sqrt\{2\}),\backslash \; \backslash pm(1+2\backslash sqrt\{2\}),\backslash \; \backslash pm(1+2\backslash sqrt\{2\})\backslash right)$

{{5-cube Coxeter plane graphs|t023|150}}

• Runcicantitruncated penteract
• Biruncicantitruncated pentacross
• great prismated penteract ({{not a typo|gippin}}) (Jonathan Bowers)

The Cartesian coordinates of the vertices of a runcicantitruncated 5-cube having an edge length of 2 are given by all permutations of coordinates and sign of:

:$\backslash left(1,\backslash \; 1+\backslash sqrt\{2\},\backslash \; 1+2\backslash sqrt\{2\},\backslash \; 1+3\backslash sqrt\{2\},\backslash \; 1+3\backslash sqrt\{2\}\backslash right)$

{{5-cube Coxeter plane graphs|t0123|150}}

These polytopes are a part of a set of 31 uniform polytera generated from the regular 5-cube or 5-orthoplex.

{{Penteract family}}

• 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, {{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]
• 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)}} o3x3o3o4x - span, o3x3o3x4x - pattin, o3x3x3o4x - prin, o3x3x3x4x - gippin

• {{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