Runcic 5-cubes

In six-dimensional geometry, a runcic 5-cube or (runcic 5-demicube, runcihalf 5-cube) is a convex uniform 5-polytope. There are 2 runcic forms for the 5-cube. Runcic 5-cubes have half the vertices of runcinated 5-cubes.

Alternate names

 * Cantellated 5-demicube/demipenteract
 * Small rhombated hemipenteract (sirhin) (Jonathan Bowers)

Cartesian coordinates
The Cartesian coordinates for the 960 vertices of a runcic 5-cubes centered at the origin are coordinate permutations:
 * (±1,±1,±1,±3,±3)

with an odd number of plus signs.

Related polytopes
It has half the vertices of the runcinated 5-cube, as compared here in the B5 Coxeter plane projections:

Alternate names

 * Cantitruncated 5-demicube/demipenteract
 * Great rhombated hemipenteract (girhin) (Jonathan Bowers)

Cartesian coordinates
The Cartesian coordinates for the 480 vertices of a runcicantic 5-cube centered at the origin are coordinate permutations:
 * (±1,±1,±3,±5,±5)

with an odd number of plus signs.

Related polytopes
It has half the vertices of the runcicantellated 5-cube, as compared here in the B5 Coxeter plane projections:

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 5-polytopes 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.