Stericantellated 5-simplex
Stericantellated 5-simplex | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Card |
Coxeter diagram | x3o3x3o3x () |
Elements | |
Tera | 20 triangular duoprisms, 30 cuboctahedral prisms, 12 small rhombated pentachora |
Cells | 120+120 triangular prisms, 30 octahedra, 90 cubes, 60 cuboctahedra |
Faces | 120+240 triangles, 180+360 squares |
Edges | 360+360 |
Vertices | 180 |
Vertex figure | Antiduowedge, edge lengths 1 (bases of disphenoid cell and top square) and √2 (remaining edges) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Cope–trip–triddip: 135° |
Srip–co–cope: | |
cope–cube–cope: 120° | |
Srip–trip–cope: | |
Srip–oct–srip: | |
Central density | 1 |
Number of external pieces | 62 |
Level of complexity | 28 |
Related polytopes | |
Army | Card |
Regiment | Card |
Dual | Anticupolanotched hecatonoctacontateron |
Conjugate | None |
Abstract & topological properties | |
Flag count | 40320 |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | A5×2, order 1440 |
Convex | Yes |
Nature | Tame |
The stericantellated 5-simplex, also called the cellirhombated hexateron, cellirhombidodecateron, or card, is a convex uniform 5-polytope. It consists of 20 triangular duoprisms, 30 cuboctahedral prisms, and 12 small rhombated pentachora. 1 triangular duoprism, 2 small rhombated pentachora, and 4 cuboctahedral prisms join at each vertex. As the name suggests, it is the stericantellation of the 5-simplex.
Vertex coordinates[edit | edit source]
The vertices of a stericantellated 5-simplex of edge length 1 can be given in 6 dimensions as all permutations of:
- .
Representations[edit | edit source]
A stericantellated 5-simplex has the following Coxeter diagrams:
- x3o3x3o3x () (full symmetry)
- xxxo3xxoo3ooxx3oxxx&#xt (A4 axial, small rhombated pentachoron-first)
- x(uo)(xd)(uo)x x(xx)(xo)(ou)x3o(xo)(xx)(xo)o3x(ou)(xo)(xx)x&#xt (A3×A1 axial, cuboctahedral prism-first)
Gallery[edit | edit source]
-
A4 orthographic projection
-
A3
-
A2
Related polytopes[edit | edit source]
The stericantellated 5-simplex is the colonel of a regiment of 18 members. Of these, 9 have full symmetry, while the other 9 have single A5 symmetry only.
External links[edit | edit source]
- Klitzing, Richard. "card".
- Wikipedia contributors. "Stericantellated 5-simplex".