Bicantellated 5-cube
Bicantellated 5-cube | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Sibrant |
Coxeter diagram | o4x3o3x3o () |
Elements | |
Tera | 80 triangular-square duoprisms, 32 small rhombated pentachora, 10 rectified icositetrachora |
Cells | 320 triangular prisms, 80 octahedra, 240 cubes, 40+160 cuboctahedra |
Faces | 320+320+320 triangles, 240+960 squares |
Edges | 960+960 |
Vertices | 480 |
Vertex figure | Digonal disphenoidal prism, edge lengths 1 (base square and two edges of rectangle base) and √2 (sides and other edges of base rectangle) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Rico–cube–tisdip: |
Srip–trip–tisdip: | |
Srip–oct–srip: | |
Rico–co–srip: | |
Rico–co–rico: 90° | |
Central density | 1 |
Number of external pieces | 122 |
Level of complexity | 24 |
Related polytopes | |
Army | Sibrant |
Regiment | Sibrant |
Dual | Disphenoidal tegmatic tetracosioctacontateron |
Conjugate | None |
Abstract & topological properties | |
Flag count | 92160 |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | B5, order 3840 |
Convex | Yes |
Nature | Tame |
The bicantellated 5-cube, also called the small birhombipenteractitriacontaditeron or sibrant, is a convex uniform 5-polytope. It consists of 80 triangular-square duoprisms, 32 small rhombated pentachora, and 10 rectified icositetrachora. 2 triangular-square duoprisms, 2 small rhombated pentachora, and 2 rectified icositetrachora join at each vertex. As the name suggests, it is the bicantellation of the 5-cube, or equivalently of its dual 5-orthoplex.
Vertex coordinates[edit | edit source]
The vertices of a bicantellated 5-cube of edge length 1 are given by all permutations of:
- .
Representations[edit | edit source]
A bicantellated 5-cube has the following Coxeter diagrams:
- o4x3o3x3o () (full symmetry)
- x3o3x3o *b3x () (D5 symmetry, as cantellated demipenteract)
- s4x3o3x3o () (D5 symmetry, as alternated faceting)
- ooqoo4xxoxx3oxxxo3xooox&#xt (B4 axial, rectified icositetrachoron-first)
Gallery[edit | edit source]
-
B4 or D5 orthographic projection
-
B3, D4, or A2
-
B2
-
A3
Related polytopes[edit | edit source]
The regiment of the bicantellated 5-cube includes a total of 47 members. Of these, 31 have full symetry, while the remaining 16 have D5 symmetry only.
External links[edit | edit source]
- Klitzing, Richard. "sibrant".
- Wikipedia contributors. "Bicantellated 5-cube".