stericated 5-cubes

• Stericated penteract / Stericated 5-orthoplex / Stericated pentacross
• Expanded penteract / Expanded 5-orthoplex / Expanded pentacross
• Small cellated penteractitriacontaditeron (Acronym: scant) (Jonathan Bowers)Klitzing, (x3o3o3o4x - scant)

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

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

The stericated 5-cube is constructed by a sterication operation applied to the 5-cube.

The stericated 5-cube can be dissected into two tesseractic cupolae and a runcinated tesseract between them. This dissection can be seen as analogous to the 4D runcinated tesseract being dissected into two cubic cupolae and a central rhombicuboctahedral prism between them, and also the 3D rhombicuboctahedron being dissected into two square cupolae with a central octagonal prism between them.{{5-cube Coxeter plane graphs|t04|150}}

• Steritruncated penteract
• Celliprismated triacontaditeron (Acronym: capt) (Jonathan Bowers)Klitzing, (x3o3o3x4x - capt)

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

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

{{5-cube Coxeter plane graphs|t014|150}}

• Stericantellated penteract
• Stericantellated 5-orthoplex, stericantellated pentacross
• Cellirhombated penteractitriacontiditeron (Acronym: carnit) (Jonathan Bowers)Klitzing, (x3o3x3o4x - carnit)

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

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

{{5-cube Coxeter plane graphs|t024|150}}

• Stericantitruncated penteract
• Steriruncicantellated triacontiditeron / Biruncicantitruncated pentacross
• Celligreatorhombated penteract (cogrin) (Jonathan Bowers)Klitzing, (x3o3x3x4x - cogrin)

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

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

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

• Steriruncitruncated penteract / Steriruncitruncated 5-orthoplex / Steriruncitruncated pentacross
• Celliprismatotruncated penteractitriacontiditeron (captint) (Jonathan Bowers)Klitzing, (x3x3o3x4x - captint)

The Cartesian coordinates of the vertices of a steriruncitruncated penteract having an edge length of 2 are given by all permutations of coordinates and sign of:

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

{{5-cube Coxeter plane graphs|t0134|150}}

• Steritruncated pentacross
• Celliprismated penteract (Acronym: cappin) (Jonathan Bowers)Klitzing, (x3x3o3o4x - cappin)

Cartesian coordinates for the vertices of a steritruncated 5-orthoplex, centered at the origin, are all permutations of

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

{{5-cube Coxeter plane graphs|t034|150}}

• Stericantitruncated pentacross
• Celligreatorhombated triacontaditeron (cogart) (Jonathan Bowers)Klitzing, (x3x3x3o4x - cogart)

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

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

{{5-cube Coxeter plane graphs|t0234|150}}

• Steriruncicantitruncated 5-cube (Full expansion of omnitruncation for 5-polytopes by Johnson)
• Omnitruncated penteract
• Omnitruncated triacontiditeron / omnitruncated pentacross
• Great cellated penteractitriacontiditeron (Jonathan Bowers)Klitzing, (x3x3x3x4x - gacnet)

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

:$\backslash left(1,\backslash \; 1+\backslash sqrt\{2\},\backslash \; 1+2\backslash sqrt\{2\},\backslash \; 1+3\backslash sqrt\{2\},\backslash \; 1+4\backslash sqrt\{2\}\backslash right)$

{{5-cube Coxeter plane graphs|t01234|150}}

The full snub 5-cube or omnisnub 5-cube, defined as an alternation of the omnitruncated 5-cube is not uniform, but it can be given Coxeter diagram {{CDD|node_h|4|node_h|3|node_h|3|node_h|3|node_h}} and symmetry [4,3,3,3]⁺, and constructed from 10 snub tesseracts, 32 snub 5-cells, 40 snub cubic antiprisms, 80 snub tetrahedral antiprisms, 80 3-4 duoantiprisms, and 1920 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, editied 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)}} x3o3o3o4x - scan, x3o3o3x4x - capt, x3o3x3o4x - carnit, x3o3x3x4x - cogrin, x3x3o3x4x - captint, x3x3x3x4x - gacnet, x3x3x3o4x - cogart

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

{{Polytopes}}

Category:5-polytopes