Steriruncitruncated 5-cube
Steriruncitruncated 5-cube | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Captint |
Coxeter diagram | x4x3o3x3x () |
Elements | |
Tera | 80 truncated tetrahedral prisms, 80 hexagonal-octagonal duoprisms, 40 truncated cubic prisms, 32 prismatorhombated pentachora, 10 prismatorhombated hexadecachora |
Cells | 320+320 triangular prisms, 320+320 hexagonal prisms, 160 truncated tetrahedra, 240+240 octagonal prisms, 160 cuboctahedra, 80 truncated cubes |
Faces | 640+640 triangles, 480+960+960+960 squares, 640 hexagons, 480 octagons |
Edges | 960+960+1920+1920 |
Vertices | 1920 |
Vertex figure | Skewed rectangular pyramidal pyramid, base edge lengths 1 and √2, remaining edge lengths √2 (5), √3 (2), and √2+√2 (2) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Prip–tut–tuttip: |
Tuttip–hip–hodip: 150° | |
Ticcup–op–hodip: | |
Prip–hip–hodip: | |
Proh–tic–ticcup: 135° | |
Prip–trip–ticcup: | |
Proh–op–hodip: | |
Proh–trip–tuttip: 120° | |
Proh–co–prip: | |
Central density | 1 |
Number of external pieces | 242 |
Level of complexity | 80 |
Related polytopes | |
Army | Captint |
Regiment | Captint |
Dual | Small rhombipyramidal pyramidal chilliaenneacosicosateron |
Conjugate | Quasicelliprismatotruncatopenteractitriacontaditeron |
Abstract & topological properties | |
Flag count | 307200 |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | B5, order 3840 |
Convex | Yes |
Nature | Tame |
The steriruncitruncated 5-cube, also called the celliprismatotruncated penteractitriacontaditeron, celliprismatotruncatopenteractitriacontaditeron, or captint, is a convex uniform 5-polytope. It consists of 80 truncated tetrahedral prisms, 80 hexagonal-octagonal duoprisms, 40 truncated cubic prisms, 32 prismatorhombated pentachora, and 10 prismatorhombated hexadecachora. 1 prismatorhombated pentachoron, 1 prismatorhombated hexadecachoron, 1 truncated tetrahedral prism, 1 truncated cubic prism, and 2 hexagonal-octagonal duoprisms join at each vertex. As the name suggests, it is the steriruncitruncation of the 5-cube.
Vertex coordinates[edit | edit source]
The vertices of a steriruncitruncated 5-cube of edge length 1 are given by all permutations of:
- .
Gallery[edit | edit source]
-
B4 or D5 orthographic projection
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B3, D4, or A2
-
B2
-
A3
Related polytopes[edit | edit source]
The steriruncitruncated 5-cube is the colonel of a three-member regiment that also includes the small retrocelliprismatotruncatopenteractitriacontaditeron and small lepidocelliprismatotruncatopenteractitriacontaditeron.
External links[edit | edit source]
- Bowers, Jonathan. "Category 13: Prismatorhombates and Kin" (#853).
- Klitzing, Richard. "captint".
- Wikipedia contributors. "Steriruncitruncated 5-cube".