In six-dimensional geometry, a runcic 6-cube is a convex uniform 6-polytope. There are 2 unique runcic for the 6-cube.
The Cartesian coordinates for the vertices of a runcic 6-cube centered at the origin are coordinate permutations:
with an odd number of plus signs.
The Cartesian coordinates for the vertices of a runcicantic 6-cube centered at the origin are coordinate permutations:
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:
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