Stericated 5-cubes


In five-dimensional geometry, a stericated 5-cube is a convex uniform 5-polytope with fourth-order truncations of the regular 5-cube.
There are eight degrees of sterication for the 5-cube, including permutations of runcination, cantellation, and truncation. The simple stericated 5-cube is also called an expanded 5-cube, with the first and last nodes ringed, for being constructible by an expansion operation applied to the regular 5-cube. The highest form, the steriruncicantitruncated 5-cube, is more simply called an omnitruncated 5-cube with all of the nodes ringed.

Stericated 5-cube

Alternate names

The Cartesian coordinates of the vertices of a stericated 5-cube having edge length 2 are all permutations of:

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The stericated 5-cube is constructed by a sterication operation applied to the 5-cube.

Steritruncated 5-cube

Alternate names

The Cartesian coordinates of the vertices of a steritruncated 5-cube having edge length 2 are all permutations of:

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Stericantellated 5-cube

Alternate names

The Cartesian coordinates of the vertices of a stericantellated 5-cube having edge length 2 are all permutations of:

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Stericantitruncated 5-cube

Alternate names

The Cartesian coordinates of the vertices of an stericantitruncated 5-cube having an edge length of 2 are given by all permutations of coordinates and sign of:

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Steriruncitruncated 5-cube

Alternate names

The Cartesian coordinates of the vertices of an steriruncitruncated penteract having an edge length of 2 are given by all permutations of coordinates and sign of:

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Steritruncated 5-orthoplex

Alternate names

for the vertices of a steritruncated 5-orthoplex, centered at the origin, are all permutations of

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Stericantitruncated 5-orthoplex

Alternate names

The Cartesian coordinates of the vertices of an stericantitruncated 5-orthoplex having an edge length of 2 are given by all permutations of coordinates and sign of:

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Omnitruncated 5-cube

Alternate names

The Cartesian coordinates of the vertices of an omnitruncated 5-cube having an edge length of 2 are given by all permutations of coordinates and sign of:

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Full snub 5-cube

The full snub 5-cube or omnisnub 5-cube, defined as an alternation of the omnitruncated 5-cube is not uniform, but it can be given Coxeter diagram and symmetry +, and constructed from 10 snub tesseracts, 32 snub 5-cells, 40 snub cubic antiprisms, 80 snub tetrahedral antiprisms, 80 3-4 duoantiprisms, and 1920 irregular 5-cells filling the gaps at the deleted vertices.

Related polytopes

This polytope is one of 31 uniform 5-polytopes generated from the regular 5-cube or 5-orthoplex.