Steric 5-cubes


In five-dimensional geometry, a steric 5-cube or is a convex uniform 5-polytope. There are unique 4 steric forms of the 5-cube. Steric 5-cubes have half the vertices of stericated 5-cubes.

Steric 5-cube

Alternate names

Cartesian coordinates

The Cartesian coordinates for the 80 vertices of a steric 5-cube centered at the origin are the permutations of
with an odd number of plus signs.

Stericantic 5-cube

Alternate names

  • Prismatotruncated hemipenteract

Cartesian coordinates

The Cartesian coordinates for the 480 vertices of a stericantic 5-cube centered at the origin are coordinate permutations:
with an odd number of plus signs.

Steriruncic 5-cube

Alternate names

  • Prismatorhombated hemipenteract

Cartesian coordinates

The Cartesian coordinates for the 320 vertices of a steriruncic 5-cube centered at the origin are coordinate permutations:
with an odd number of plus signs.

Steriruncicantic 5-cube

Alternate names

  • Great prismated hemipenteract

Cartesian coordinates

The Cartesian coordinates for the 960 vertices of a steriruncicantic 5-cube centered at the origin are coordinate permutations:
with an odd number of plus signs.

Related polytopes

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 polytera that can be constructed from the D symmetry of the 5-demicube, of which are unique to this family, and 15 are shared within the 5-cube family.