Steriruncinated 6-cube
Steriruncinated 6-cube | |
---|---|
Rank | 6 |
Type | Uniform |
Notation | |
Bowers style acronym | Copox |
Coxeter diagram | x4o3o3x3x3o () |
Elements | |
Peta | 160 triangular-cubic duoprisms 192 decachoric prisms 240 square-truncated tetrahedral duoprisms 64 bitruncated hexatera 12 celliprismated penteracts |
Tera | 960 triangular-square duoprisms 480 tesseracts 384 truncated pentachora 960 square-hexagonal duoprisms 960+960 truncated tetrahedral prisms 384 decachora 60 small disprismatotesseractihexadecachora |
Cells | 960 tetrahedra 1920+1920 triangular prisms 480+1440+2880 cubes 3840 hexagonal prisms 960+1920 truncated tetrahedra |
Faces | 1280+3840 triangles, 2880+5760+5760 squares, 3840 hexagons |
Edges | 3840+5760+5760 |
Vertices | 3840 |
Vertex figure | Triangular 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 angles | Bittix–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 density | 1 |
Number of external pieces | 668 |
Level of complexity | 120 |
Related polytopes | |
Army | Copox |
Regiment | Copox |
Conjugate | Celliquasiprismated hexeract |
Abstract & topological properties | |
Flag count | 5529600 |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | B6, order 46080 |
Convex | Yes |
Nature | Tame |
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]
-
B5 orthographic projection
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B4
-
B3
-
B2
-
A5
-
A3
Related polytopes[edit | edit source]
The regiment of the celliprismated hexeract contains 7 uniform members.
External links[edit | edit source]
- Klitzing, Richard. "copox".
- Wikipedia contributors. "Steriruncinated 6-cube".