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In five-dimensional geometry, a steric 5-cube or (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.
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Alternate names
Cartesian coordinates
The Cartesian coordinates for the 80 vertices of a steric 5-cube centered at the origin are the permutations of
(±1,±1,±1,±1,±3)with an odd number of plus signs.
Alternate names
Cartesian coordinates
The Cartesian coordinates for the 480 vertices of a stericantic 5-cube centered at the origin are coordinate permutations:
(±1,±1,±3,±3,±5)with an odd number of plus signs.
Alternate names
Cartesian coordinates
The Cartesian coordinates for the 320 vertices of a steriruncic 5-cube centered at the origin are coordinate permutations:
(±1,±1,±1,±3,±5)with an odd number of plus signs.
Alternate names
Cartesian coordinates
The Cartesian coordinates for the 960 vertices of a steriruncicantic 5-cube centered at the origin are coordinate permutations:
(±1,±1,±3,±5,±7)with an odd number of plus signs.
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 polytera (uniform 5-polytope) 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.