Steric 6-cubes


In six-dimensional geometry, a steric 6-cube is a convex uniform 6-polytope. There are unique 4 steric forms of the 6-cube.

Steric 6-cube

Alternate names

Cartesian coordinates

The Cartesian coordinates for the 480 vertices of a steric 6-cube centered at the origin are coordinate permutations:
with an odd number of plus signs.

Stericantic 6-cube

Alternate names

  • Runcitruncated demihexeract
  • Runcitruncated 6-demicube
  • Prismatotruncated hemihexeract

Cartesian coordinates

The Cartesian coordinates for the 2880 vertices of a stericantic 6-cube centered at the origin are coordinate permutations:
with an odd number of plus signs.

Steriruncic 6-cube

Alternate names

  • Runcicantellated demihexeract
  • Runcicantellated 6-demicube
  • Prismatorhombated hemihexeract

Cartesian coordinates

The Cartesian coordinates for the 1920 vertices of a steriruncic 6-cube centered at the origin are coordinate permutations:
with an odd number of plus signs.

Steriruncicantic 6-cube

Alternate names

  • Runcicantitruncated demihexeract
  • Runcicantitruncated 6-demicube
  • Great prismated hemihexeract

Cartesian coordinates

The Cartesian coordinates for the 5760 vertices of a steriruncicantic 6-cube centered at the origin are coordinate permutations:
with an odd number of plus signs.

Related polytopes

There are 47 uniform polytopes with D6 symmetry, 31 are shared by the B6 symmetry, and 16 are unique: