In seven-dimensional geometry, a hexic 7-cube is a convex uniform 7-polytope, constructed from the uniform 7-demicube. There are 16 unique forms.
Hexic 7-cubes Wikipedia
The Cartesian coordinates for the vertices of a hexic 7-cube centered at the origin are coordinate permutations:
with an odd number of plus signs.
This polytope is based on the 7-demicube, a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.
There are 95 uniform polytopes with D7 symmetry, 63 are shared by the BC7 symmetry, and 32 are unique: