Cantic 8-cube
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| Cantic 8-cube | |
|---|---|
| D8 Coxeter plane projection | |
| Type | uniform 8-polytope |
| Schläfli symbol | t0,1{3,35,1} h2{4,3,3,3,3,3,3} |
| Coxeter-Dynkin diagram | |
| 7-faces | 16 truncated 7-demicubes 128 truncated 7-simplexes 128 rectified 7-simplexes |
| 6-faces | 112 truncated 6-demicubes 1024 truncated 6-simplexes 1024 rectified 6-simplexes 1024 6-simplexes |
| 5-faces | 448 truncated 5-demicubes 3584 truncated 5-simplexes 3584 rectified 5-simplexes 7168 5-simplexes |
| 4-faces | 1120 truncated 16-cells 7168 truncated 5-cells 7168 rectified 5-cells 21504 5-cells |
| Cells | 1792 truncated tetrahedra 8960 truncated tetrahedra 8960 octahedra 35840 tetrahedra |
| Faces | 7168 hexagons 7168 triangles 35840 triangles |
| Edges | 1792 segments 21504 segments |
| Vertices | 3584 |
| Vertex figure | ( )v{ }x{3,3,3,3} |
| Coxeter groups | D8, [35,1,1] |
| Properties | convex |
In eight-dimensional geometry, a cantic 8-cube or truncated 8-demicube is a uniform 8-polytope, being a truncation of the 8-demicube.
Alternate names
- Truncated demiocteract
- Truncated hemiocteract; Acronym: thocto (Jonathan Bowers)
Cartesian coordinates
The Cartesian coordinates for the vertices of a truncated 8-demicube centered at the origin and edge length 6√2 are coordinate permutations:
(±1,±1,±3,±3,±3,±3,±3,±3)
with an odd number of plus signs.
Images
| Coxeter plane | B8 | D8 | D7 | D6 | D5 |
|---|---|---|---|---|---|
| Graph | |||||
| Dihedral symmetry | [16/2] | [14] | [12] | [10] | [8] |
| Coxeter plane | D4 | D3 | A7 | A5 | A3 |
| Graph | |||||
| Dihedral symmetry | [6] | [4] | [8] | [6] | [4] |
Notes
- H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, , ISBN 978-0-471-01003-6 (Paper 22) H.S.M. Coxeter, Regular and Semi-Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10] (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559–591] (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3–45]
- Norman Johnson Uniform Polytopes, Manuscript (1991) N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D.
- Klitzing, Richard. . x3x3o *b3o3o3o3o3o - thocto
External links
| vteFundamental convex regular and uniform polytopes in dimensions 2–10 | |||||
|---|---|---|---|---|---|
| Family | An | Bn | I2(p) / Dn | E6 / E7 / E8 / F4 / G2 | Hn |
| Regular polygon | Triangle | Square | p-gon | Hexagon | Pentagon |
| Uniform polyhedron | Tetrahedron | Octahedron • Cube | Demicube | Dodecahedron • Icosahedron | |
| Uniform polychoron | Pentachoron | 16-cell • Tesseract | Demitesseract | 24-cell | 120-cell • 600-cell |
| Uniform 5-polytope | 5-simplex | 5-orthoplex • 5-cube | 5-demicube | ||
| Uniform 6-polytope | 6-simplex | 6-orthoplex • 6-cube | 6-demicube | 122 • 221 | |
| Uniform 7-polytope | 7-simplex | 7-orthoplex • 7-cube | 7-demicube | 132 • 231 • 321 | |
| Uniform 8-polytope | 8-simplex | 8-orthoplex • 8-cube | 8-demicube | 142 • 241 • 421 | |
| Uniform 9-polytope | 9-simplex | 9-orthoplex • 9-cube | 9-demicube | ||
| Uniform 10-polytope | 10-simplex | 10-orthoplex • 10-cube | 10-demicube | ||
| Uniform n-polytope | n-simplex | n-orthoplex • n-cube | n-demicube | 1k2 • 2k1 • k21 | n-pentagonal polytope |
| Topics: Polytope families • Regular polytope • List of regular polytopes and compounds • Polytope operations |