Cantic 8-cube

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
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
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 (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

orthographic projections

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]

References

• 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 [1]
    • (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. "8D uniform polytopes (polyzetta) x3x3o *b3o3o3o3o3o".

External links

• Weisstein, Eric W. "Hypercube". MathWorld.
• Polytopes of Various Dimensions
• Multi-dimensional Glossary