Cantic 5-cube


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 are coordinate permutations:
with an odd number of plus signs.

Alternate names

Related polytopes

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-polytope 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.