Truncated 5-demicube
Cantic 5-cube

D5 Coxeter plane projection
Typeuniform 5-polytope
Schläfli symbolh2{4,3,3,3}
t{3,32,1}
Coxeter-Dynkin diagram=
4-faces42 total:
16 r{3,3,3}
16 t{3,3,3}
10 t{3,3,4}
Cells280 total:
80 {3,3}
120 t{3,3}
80 {3,4}
Faces640 total:
480 {3}
160 {6}
Edges560
Vertices160
Vertex figure
( )v{ }×{3}
Coxeter groupsD5, [32,1,1]
Propertiesconvex

In geometry of five dimensions or higher, a cantic 5-cube, cantihalf 5-cube, truncated 5-demicube is a uniform 5-polytope, being a truncation of the 5-demicube. It has half the vertices of a cantellated 5-cube.

Cartesian coordinates

The Cartesian coordinates for the 160 vertices of a cantic 5-cube centered at the origin and edge length 6√2 are coordinate permutations:

(±1,±1,±3,±3,±3)

with an odd number of plus signs.

Alternate names

  • Cantic penteract, truncated demipenteract
  • Truncated hemipenteract (thin) (Jonathan Bowers)[1]

It has half the vertices of the cantellated 5-cube, as compared here in the B5 Coxeter plane projections:


Cantic 5-cube
Cantellated 5-cube

This polytope is based on the 5-demicube, a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.

There are 23 uniform 5-polytopes that can be constructed from the D5 symmetry of the 5-demicube, of which are unique to this family, and 15 are shared within the 5-cube family.

Notes

  1. ^ Klitzing, pp. (x3x3o *b3o3o - thin).

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 Ivić Weiss, Wiley-Interscience Publication, 1995, wiley.com, 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.
  • x3x3o *b3o3o - thin