Cantitruncated 5-simplex
(Redirected from Great rhombated hexateron)
Cantitruncated 5-simplex | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Garx |
Coxeter diagram | x3x3x3o3o () |
Elements | |
Tera | 15 tetrahedral prisms, 6 truncated pentachora, 6 great rhombated pentachora |
Cells | 30 tetrahedra, 60 triangular prisms, 30 truncated tetrahedra, 15 truncated octahedra |
Faces | 120 triangles, 90 squares, 20+60 hexagons |
Edges | 60+60+180 |
Vertices | 120 |
Vertex figure | Triangular pyramidal pyramid, edge lengths 1 (base), √2 (sides of pyramid 1), and √3 (sides of pyramid 2 and lacing between apices) |
Measures (edge length 1) | |
Circumradius | 2 |
Hypervolume | |
Diteral angles | Tip–tet–tepe: |
Grip–trip–tepe: | |
Grip–tut–tip: | |
Grip–toe–grip: | |
Central density | 1 |
Number of external pieces | 27 |
Level of complexity | 20 |
Related polytopes | |
Army | Garx |
Regiment | Garx |
Dual | Triangular-pyramidal pyramidal hecatonicosateron |
Conjugate | None |
Abstract & topological properties | |
Flag count | 14400 |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | A5, order 720 |
Convex | Yes |
Nature | Tame |
The cantitruncated 5-simplex, also called the great rhombated hexateron or garx, is a convex uniform 5-polytope. It consists of 15 tetrahedral prisms, 6 truncated pentachora, and 6 great rhombated pentachora. One truncated pentachoron, 1 tetrahedral prism, and 3 great rhombated pentachora join at each vertex. As the name suggests, it is the cantitruncation of the 5-simplex.
Vertex coordinates[edit | edit source]
The vertices of a cantitruncated 5-simplex of edge length 1 can be given in 6 dimensions as all permutations of:
- .
Representations[edit | edit source]
A cantitruncated 5-simplex has the following Coxeter diagrams:
- x3x3x3o3o () (full symmetry)
- xuxx3xxux3ooox3oooo&#xt (A4 axial, truncated pentachoron-first)
Gallery[edit | edit source]
-
A4 orthographic projection
-
A3
-
A2
External links[edit | edit source]
- Bowers, Jonathan. "Category 10: Greater Truncates" (#722).
- Klitzing, Richard. "garx".
- Wikipedia contributors. "Cantitruncated 5-simplex".