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.

Alternate names

 * Runcinated demihexeract/6-demicube
 * Small prismated hemihexeract (Acronym sophax) (Jonathan Bowers)

Cartesian coordinates
The Cartesian coordinates for the 480 vertices of a steric 6-cube centered at the origin are coordinate permutations:
 * (±1,±1,±1,±1,±1,±3)

with an odd number of plus signs.

Alternate names

 * Runcitruncated demihexeract/6-demicube
 * Prismatotruncated hemihexeract (Acronym pithax) (Jonathan Bowers)

Cartesian coordinates
The Cartesian coordinates for the 2880 vertices of a stericantic 6-cube centered at the origin are coordinate permutations:
 * (±1,±1,±1,±3,±3,±5)

with an odd number of plus signs.

Alternate names

 * Runcicantellated demihexeract/6-demicube
 * Prismatorhombated hemihexeract (Acronym prohax) (Jonathan Bowers)

Cartesian coordinates
The Cartesian coordinates for the 1920 vertices of a steriruncic 6-cube centered at the origin are coordinate permutations:
 * (±1,±1,±1,±1,±3,±5)

with an odd number of plus signs.

Alternate names

 * Runcicantitruncated demihexeract/6-demicube
 * Great prismated hemihexeract (Acronym gophax) (Jonathan Bowers)

Cartesian coordinates
The Cartesian coordinates for the 5760 vertices of a steriruncicantic 6-cube centered at the origin are coordinate permutations:
 * (±1,±1,±1,±3,±5,±7)

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: