Bicantellated 5-simplex
Bicantellated 5-simplex | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Sibrid |
Coxeter diagram | o3x3o3x3o () |
Elements | |
Tera | 20 triangular duoprisms, 12 small rhombated pentachora |
Cells | 120 triangular prisms, 30 octahedra, 30 cuboctahedra |
Faces | 120+120 triangles, 180 squares |
Edges | 360 |
Vertices | 90 |
Vertex figure | Tetragonal disphenoidal prism, edge lengths 1 (base squares) and √2 (sides) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Srip–trip–triddip: |
Srip–co–srip: | |
Srip–oct–srip: | |
Central density | 1 |
Number of external pieces | 32 |
Level of complexity | 12 |
Related polytopes | |
Army | Sibrid |
Regiment | Sibrid |
Dual | Disphenoidal tegmatic enneacontateron |
Conjugate | None |
Abstract & topological properties | |
Flag count | 17280 |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | A5×2, order 1440 |
Convex | Yes |
Nature | Tame |
The bicantellated 5-simplex, also called the small birhombated hexateron, small birhombidodecateron, or sibrid, is a convex uniform 5-polytope. It consists of 20 triangular duoprisms and 12 small rhombated pentachora. 2 triangular duoprisms and 4 small rhombated pentachora join at each vertex. As the name suggests, it is the bicantellation of the 5-simplex. It is also the rectification of the birectified 5-simplex.
Vertex coordinates[edit | edit source]
The vertices of a bicantellated 5-simplex of edge length 1 can be given in 6 dimensions as all permutations of:
- .
Representations[edit | edit source]
A bicantellated 5-simplex has the following Coxeter diagrams:
- o3x3o3x3o () (full symmetry)
- xoo3oxx3xxo3oox&#xt (A4 axial, small rhombated pentachoron-first)
Gallery[edit | edit source]
-
A4 orthographic projection
-
A3
-
A2
Related polytopes[edit | edit source]
The regiment of the bicantellated 5-simplex includes a total of 23 members. Of these, 15 have full symmetry, while the remaining 8 have single A5 symmetry only.
External links[edit | edit source]
- Klitzing, Richard. "sibrid".
- Wikipedia contributors. "Bicantellated 5-simplex".