Penticantellated 6-cube
Penticantellated 6-cube | |
---|---|
Rank | 6 |
Type | Uniform |
Notation | |
Bowers style acronym | Topag |
Coxeter diagram | x4o3x3o3o3x () |
Elements | |
Peta | 240 square-tetrahedral duoprisms 192 small prismatodecachoric prisms 160 triangular-small rhombicuboctahedral duoprisms 60 small rhombated tesseractic prisms 64 runcinated 5-simplices 12 runcinated 5-cubes |
Tera | 960+960 tetrahedral prisms 1280 triangular duoprisms 384 rectified pentachora 960+1920+1920 triangular-square duoprisms 960 octahedral prisms 384 small prismatodecachora 480 small rhombicuboctahedral prisms 120 small rhombated tesseracts |
Cells | 960+1920 tetrahedrae 5×3840 triangular prisms 1920 octahedra 1440+5760 cubes 480 small rhombicuboctahedra |
Faces | 3840+3840+7680 triangles, 960+5760+5760+11520 squares |
Edges | 3840+5760+11520 |
Vertices | 3840 |
Vertex figure | Diminished tetrahedral antifastegium, edge lengths 1 (base triangular prism and triangle of antifastegium facet) and √2 (remaining edges) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dipetal angles | Spix–spid–spiddip: |
Spiddip–tepe–squatet: | |
Trasirco–tisdip–squatet: 150° | |
Srittip–sircope–trasirco: | |
Spiddip–tisdip-trasirco: | |
Sirn–srit–srittip, Spix–triddip–trasirco: 135° | |
Spiddip–tisdip–srittip: | |
Spix–ope–srittip: | |
Central density | 1 |
Number of external pieces | 728 |
Level of complexity | 176 |
Related polytopes | |
Army | Topag |
Regiment | Topag |
Conjugate | None |
Abstract & topological properties | |
Flag count | 8524800 |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | B6, order 46080 |
Convex | Yes |
Nature | Tame |
The penticantellated 6-cube, also called the penticantellated dodecapeton, teriprismated hexacontatetrapeton, or topag, is a convex uniform 6-polytope. It consists of 12 cantellated 5-cubes, 64 runcinated 5-simplices, 192 small prismatodecachoric prisms, 60 small rhombated tesseractic prisms, 240 square-tetrahedral duoprisms, and 160 triangular-small rhombicuboctahedral duoprisms. 1 cantellated 5-cube, 1 runcinated 5-simplex, 2 small prismatodecachoric prisms, 3 small rhombated tesseractic prisms, 1 square-tetrahedral duoprism, and 3 triangular-small rhombicuboctahedral duoprisms join at each vertex. As the name suggests, it is the penticantellation of the 6-cube.
The teriprismated hexacontatetrapeton contains the vertices of an inscribed steritruncated 5-cubic prism, octagonal-prismatorhombated hexadecachoric duoprism, and truncated cubic-great rhombicuboctahedral duoprism.
Vertex coordinates[edit | edit source]
The vertex coordinates of a penticantellated 6-cube, centered at the origin and with unit edge length, are given by all permutations of:
- .
Gallery[edit | edit source]
-
B5 orthographic projection
-
B4
-
B3
-
B2
-
A5
-
A3
Related polytopes[edit | edit source]
The regiment of the teriprismated hexacontatetrapeton contains 139 uniform members plus one fissary.
External links[edit | edit source]
- Klitzing, Richard. "topag".
- Wikipedia contributors. "Penticantellated 6-cube".