In five-dimensional geometry, a steric 5-cube, steric 5-demicube or sterihalf 5-cube, is a convex uniform 5-polytope. There are unique 4 steric forms of the 5-cube. Steric 5-cubes have half the vertices of stericated 5-cubes.
The Cartesian coordinates for the 80 vertices of a steric 5-cube centered at the origin are the permutations of
with an odd number of plus signs.
The Cartesian coordinates for the 480 vertices of a stericantic 5-cube centered at the origin are coordinate permutations:
with an odd number of plus signs.
The Cartesian coordinates for the 320 vertices of a steriruncic 5-cube centered at the origin are coordinate permutations:
with an odd number of plus signs.
The Cartesian coordinates for the 960 vertices of a steriruncicantic 5-cube centered at the origin are coordinate permutations:
with an odd number of plus signs.
These polytopes are based on the 5-demicube, a member of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.
There are 23 uniform polytera (uniform 5-polytopes) that can be constructed from the D symmetry of the 5-demicube, 8 of which are unique to this family, and 15 are shared within the 5-cube family.