Cantellated 5-simplex
(Redirected from Small rhombated hexateron)
Cantellated 5-simplex | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Sarx |
Coxeter diagram | x3o3x3o3o () |
Elements | |
Tera | 15 tetrahedral prisms, 6 rectified pentachora, 6 small rhombated pentachora |
Cells | 30 tetrahedra, 60 triangular prisms, 30 octahedra, 15 cuboctahedra |
Faces | 20+60+120 triangles, 90 squares |
Edges | 60+180 |
Vertices | 60 |
Vertex figure | Triangular pyramidal prism, edge lengths 1 (base triangular prism and top edge) and √2 (sides) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Rap–tet–tepe: |
Srip–trip–tepe: | |
Srip–oct–rap: | |
Srip–co–srip: | |
Central density | 1 |
Number of external pieces | 27 |
Level of complexity | 16 |
Related polytopes | |
Army | Sarx |
Regiment | Sarx |
Dual | Triangular-pyramidal tegmatic hexecontateron |
Conjugate | None |
Abstract & topological properties | |
Flag count | 11520 |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | A5, order 720 |
Convex | Yes |
Nature | Tame |
The cantellated 5-simplex, also called the small rhombated hexateron or sarx, is a convex uniform 5-polytope. It consists of 15 tetrahedral prisms, 6 rectified pentachora, and 6 small rhombated pentachora. One rectified pentachoron, 2 tetrahedral prisms, and 3 small rhombated pentachora join at each vertex. As the name suggests, it is the cantellation of the 5-simplex.
Vertex coordinates[edit | edit source]
The vertices of a cantellated 5-simplex of edge length 1 can be given in 6 dimensions as all permutations of:
- .
Representations[edit | edit source]
A cantellated 5-simplex has the following Coxeter diagrams:
- x3o3x3o3o () (full symmetry)
- oxx3xxo3oox3ooo&#xt (A4 axial, rectified pentachoron-first)
- x(uo)xo x(ou)xx3o(xo)xo3o(oo)ox&#xt (A3×A1 axial, tetrahedral prism-first)
- ox(ou)xx3oo(xo)xo xx(uo)xo3ox(ox)oo&#xt (A2×A2 axial, triangle-first)
Gallery[edit | edit source]
-
A4 orthographic projection
-
A3
-
A2
Related polytopes[edit | edit source]
The cantellated 5-simplex is the colonel of a regiment that includes 15 uniform members.
External links[edit | edit source]
- Klitzing, Richard. "sarx".
- Wikipedia contributors. "Cantellated 5-simplex".