Stericantitruncated 5-simplex
Stericantitruncated 5-simplex | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Cograx |
Coxeter diagram | x3x3x3o3x () |
Elements | |
Tera | 20 triangular-hexagonal duoprisms, 15 cuboctahedral prisms, 15 truncated octahedral prisms, 6 great rhombated pentachora, 6 prismatorhombated pentachora |
Cells | 60+60+60 triangular prisms, 90 cubes, 60+60 hexagonal prisms, 30 truncated tetrahedra, 30 cuboctahedra, 30 truncated octahedra |
Faces | 120+120 triangles, 180+180+180+180 squares, 60+120 hexagons |
Edges | 180+180+360+360 |
Vertices | 360 |
Vertex figure | Skew rectangular pyramidal pyramid, base edge lengths 1 and √2, remaining edge lengths √2 (6) and √3 (3) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Tope–hip–thiddip: 135° |
Cope–trip–thiddip: 135° | |
Prip–co–cope: | |
Grip–toe–tope: | |
Cope–cube–tope: 120° | |
Prip–trip–thiddip: | |
Grip–trip–cope: | |
Prip–hip–tope: | |
Prip–tut–grip: | |
Central density | 1 |
Number of external pieces | 62 |
Level of complexity | 80 |
Related polytopes | |
Army | Cograx |
Regiment | Cograx |
Dual | Deltopyramidal pyramidal triacosihexecontateron |
Conjugate | None |
Abstract & topological properties | |
Flag count | 57600 |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | A5, order 720 |
Convex | Yes |
Nature | Tame |
The stericantitruncated 5-simplex, also called the celligreatorhombated hexateron or cograx, is a convex uniform 5-polytope. It consists of 20 triangular-hexagonal duoprisms, 15 cuboctahedral prisms, 15 truncated octahedral prisms, 6 great rhombated pentachora, and 6 prismatorhombated pentachora. 1 prismatorhombated pentachoron, 1 cuboctahedral prism, 1 great rhombated pentachoron, 1 triangular-hexagonal duoprism, and 2 truncated octahedral prisms join at each vertex. As the name suggests, it is the stericantitruncation of the 5-simplex.
Vertex coordinates[edit | edit source]
The vertices of a stericantitruncated 5-simplex of edge length 1 can be given in 6 dimensions as all permutations of:
- .
Gallery[edit | edit source]
-
A4 orthographic projection
-
A3
-
A2
Related polytopes[edit | edit source]
The stericantitruncated 5-simplex is the colonel of a three-member regiment that also includes the retrocelligreatorhombated hexateron and lepidocelligreatorhombated hexateron.
External links[edit | edit source]
- Bowers, Jonathan. "Category 13: Prismatorhombates and Kin" (#841).
- Klitzing, Richard. "cograx".
- Wikipedia contributors. "Stericantitruncated 5-simplex".