Runcic 6-cubes

In six-dimensional geometry, a runcic 6-cube is a convex uniform 6-polytope. There are 2 unique runcic for the 6-cube.

Alternate names

 * Cantellated 6-demicube/demihexeract
 * Small rhombated hemihexeract (Acronym sirhax) (Jonathan Bowers)

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

with an odd number of plus signs.

Alternate names

 * Cantitruncated 6-demicube/demihexeract
 * Great rhombated hemihexeract (Acronym girhax) (Jonathan Bowers)

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

with an odd number of plus signs.

Related polytopes
This polytope is based on the 6-demicube, a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.

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