Stericated 5-cube
Stericated 5-cube | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Scant |
Coxeter diagram | x4o3o3o3x () |
Elements | |
Tera | 32 pentachora, 80 tetrahedral prisms, 80 triangular-square duoprisms, 10+40 tesseracts |
Cells | 160 tetrahedra, 320 triangular prisms, 80+240 cubes |
Faces | 320 triangles, 240+480 squares |
Edges | 320+320 |
Vertices | 160 |
Vertex figure | Tetrahedral antipodium, edge lengths 1 (base 1) and √2 (base 2 and sides) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Pen–tet–tepe: |
Tepe–trip–tisdip: 150° | |
Tes–cube–tisdip: | |
Tes–cube–tes: 135° | |
Central density | 1 |
Number of external pieces | 242 |
Level of complexity | 16 |
Related polytopes | |
Army | Scant |
Regiment | Scant |
Dual | Tetrahedral-antitegmatic hecatonhexecontateron |
Conjugate | Quasicellipenteractitriacontaditeron |
Abstract & topological properties | |
Flag count | 61440 |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | B5, order 3840 |
Convex | Yes |
Nature | Tame |
The stericated 5-cube, also called the small cellated penteract, small cellipenteractitriacontaditeron, or scant, is a convex uniform 5-polytope. It consists of 32 regular pentachora, 80 tetrahedral prisms, 80 triangular-square duoprisms, and 10+40 tesseracts. 1 pentachoron, 4 tetrahedral prisms, 6 triangular-square duoprisms, and 1+4 tesseracts join at each vertex. It can be formed by expanding the facets of either the 5-cube or its dual 5-orthoplex outward.
The stericated 5-cube contains the vertices of a small disprismatotesseractihexadecachoric prism, square-small rhombicuboctahedral duoprism, and octagonal-cubic duoprism.
Vertex coordinates[edit | edit source]
The vertices of a stericated 5-cube of edge length 1 are given by all permutations of:
- .
Representations[edit | edit source]
A stericated 5-cube has the following Coxeter diagrams:
- x4o3o3o3x () (full symmetry)
- xxxx4oooo3oooo3oxxo&#xt (B4 axial, tesseract-first)
- wx xx4oo3oo3ox&#zx (B4×A1 symmetry)
- xx4ox xx4oo3xo&#zx (B3×B2 symmetry)
Gallery[edit | edit source]
-
B4 or D5 orthographic projection
-
B3, D4, or A2
-
B2
-
A3
Related polytopes[edit | edit source]
The stericated 5-cube is the colonel of a regiment that contains a total of 15 uniform members. This regiment also has many subsymmetric scaliform members.
External links[edit | edit source]
- Bowers, Jonathan. "Category 9: Podiumverts" (#692).
- Klitzing, Richard. "scant".
- Wikipedia contributors. "Stericated 5-cube".