Cantic 8-cube explained

bgcolor=#e7dcc3 colspan=2	Cantic 8-cube
bgcolor=#ffffff align=center colspan=2	D8 Coxeter plane projection
Type	uniform 8-polytope
Schläfli symbol	t_0,1 h₂
Coxeter-Dynkin diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure	vx
Coxeter groups	D₈, [3<sup>5,1,1</sup>]
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

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.

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, http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html
  - (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.