Steriruncinated 6-cube

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Steriruncinated 6-cube
Rank6
TypeUniform
Notation
Bowers style acronymCopox
Coxeter diagramx4o3o3x3x3o ()
Elements
Peta160 triangular-cubic duoprisms
192 decachoric prisms
240 square-truncated tetrahedral duoprisms
64 bitruncated hexatera
12 celliprismated penteracts
Tera960 triangular-square duoprisms
480 tesseracts
384 truncated pentachora
960 square-hexagonal duoprisms
960+960 truncated tetrahedral prisms
384 decachora
60 small disprismatotesseractihexadecachora
Cells960 tetrahedra
1920+1920 triangular prisms
480+1440+2880 cubes
3840 hexagonal prisms
960+1920 truncated tetrahedra
Faces1280+3840 triangles, 2880+5760+5760 squares, 3840 hexagons
Edges3840+5760+5760
Vertices3840
Vertex figureTriangular antipodial scalene, base edge lengths 1 (one base) and 2 (remaining edges), opposite edge length 1, lacing lengths 2 and 3
Measures (edge length 1)
Circumradius
Hypervolume
Dipetal anglesBittix–deca–decap:
 Decap–tutip–squatut:
 Tracube–tisdip–squatut: 150°
 Cappin–tes–tracube:
 Cappin–shiddip–squatut: 120°
 Cappin–tuttip–decap:
 Cappin–tip–bittix:
 Cappin–sidpith–cappin: 90°
Central density1
Number of external pieces668
Level of complexity120
Related polytopes
ArmyCopox
RegimentCopox
ConjugateCelliquasiprismated hexeract
Abstract & topological properties
Flag count5529600
Euler characteristic0
OrientableYes
Properties
SymmetryB6, order 46080
ConvexYes
NatureTame

The steriruncinated 6-cube, also called the steriruncinated dodecapeton, celliprismated hexeract, or copox, is a convex uniform 6-polytope. It consists of 12 steritruncated 5-orthoplexes, 64 bitruncated 5-simplices, 192 decachoric prisms, 240 square-truncated tetrahedral duoprisms, and 160 triangular-cubic duoprisms. 2 steritruncated 5-orthoplexes, 1 bitruncated 5-simplex, 3 decachoric prisms, 3 square-truncated tetrahedral duoprisms, and 1 triangular-cubic duoprism join at each vertex. As the name suggests, it is the steriruncination of the 6-cube.

The celliprismated hexeract contains the vertices of an inscribed prismatorhombated penteractic prism and square-great rhombated tesseractic duoprism.

Vertex coordinates[edit | edit source]

The coordinates of a steriruncinated 6-cube, centered at the origin and with unit edge length, are given by all permutations of:

  • .

Gallery[edit | edit source]

Related polytopes[edit | edit source]

The regiment of the celliprismated hexeract contains 7 uniform members.

External links[edit | edit source]