Runcinated 5-simplex
Runcinated 5-simplex | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Spix |
Coxeter diagram | x3o3o3x3o () |
Elements | |
Tera | 20 triangular duoprisms, 15 octahedral prisms, 6 rectified pentachora, 6 small prismatodecachora |
Cells | 15+30 tetrahedra, 60+60+60 triangular prisms, 30 octahedra |
Faces | 60+60+120 triangles, 180 squares |
Edges | 90+180 |
Vertices | 60 |
Vertex figure | Triangular antifastegium, edge lengths 1 (base triangular prism and top triangle) and √2 (sides) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Ope–trip–triddip: 135° |
Rap–oct–ope: | |
Spid–trip–triddip: | |
Spid–trip–ope: | |
Spid–tet–rap: | |
Spid–tet–spid: | |
Central density | 1 |
Number of external pieces | 47 |
Level of complexity | 25 |
Related polytopes | |
Army | Spix |
Regiment | Spix |
Dual | Antitegmatonotched hexecontateron |
Conjugate | None |
Abstract & topological properties | |
Flag count | 18000 |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | A5, order 720 |
Convex | Yes |
Nature | Tame |
The runcinated 5-simplex, also called the small prismated hexateron or spix, is a convex uniform 5-polytope. It consists of 20 triangular duoprisms, 15 octahedral prisms, 6 rectified pentachora, and 6 small prismatodecachora. One rectified pentachoron, 2 small prismatodecachora, 3 octahedral prisms, and 3 triangular duoprisms join at each vertex. As the name suggests, it is the runcination of the 5-simplex.
Vertex coordinates[edit | edit source]
The vertices of a runcinated 5-simplex of edge length 1 can be given in 6 dimensions as all permutations of:
- .
Representations[edit | edit source]
A runcinated 5-simplex has the following Coxeter diagrams:
- x3o3o3x3o () (full symmetry)
- oox3xxo3ooo3oxx&#xt (A4 axial, rectified pentachoron-first)
Gallery[edit | edit source]
-
A4 orthographic projection
-
A3
-
A2
Related polytopes[edit | edit source]
The regiment of the runcinated 5-simplex includes a total of 37 members plus one fissary member. This makes it the largest regiment of uniform polytera with A5 symmetry.
External links[edit | edit source]
- Klitzing, Richard. "spix".
- Wikipedia contributors. "Runcinated 5-simplex".