In five-dimensional geometry, a stericated 5-cube is a convex uniform 5-polytope with fourth-order truncations (sterication) 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
Stericated penteract / Stericated 5-orthoplex / Stericated pentacross
Expanded penteract / Expanded 5-orthoplex / Expanded pentacross
Small cellated penteractitriacontaditeron (Acronym: scant) (Jonathan Bowers)
Coordinates
The Cartesian coordinates of the vertices of a stericated 5-cube having edge length 2 are all permutations of:
Images
The stericated 5-cube is constructed by a sterication operation applied to the 5-cube.
Steritruncated 5-cube
Alternate names
Steritruncated penteract
Celliprismated triacontaditeron (Acronym: capt) (Jonathan Bowers)
Construction and coordinates
The Cartesian coordinates of the vertices of a steritruncated 5-cube having edge length 2 are all permutations of:
Images
Stericantellated 5-cube
Alternate names
Stericantellated penteract
Stericantellated 5-orthoplex, stericantellated pentacross
Cellirhombated penteractitriacontiditeron (Acronym: carnit) (Jonathan Bowers)
Coordinates
The Cartesian coordinates of the vertices of a stericantellated 5-cube having edge length 2 are all permutations of:
Images
Stericantitruncated 5-cube
Alternate names
Stericantitruncated penteract
Steriruncicantellated triacontiditeron / Biruncicantitruncated pentacross
Celligreatorhombated penteract (cogrin) (Jonathan Bowers)
Coordinates
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:
Images
Steriruncitruncated 5-cube
Alternate names
Steriruncitruncated penteract / Steriruncitruncated 5-orthoplex / Steriruncitruncated pentacross Celliprismatotruncated penteractitriacontiditeron (captint) (Jonathan Bowers)
Coordinates
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:
Images
Steritruncated 5-orthoplex
Alternate names
Steritruncated pentacross
Celliprismated penteract (Acronym: cappin) (Jonathan Bowers)
Coordinates
Cartesian coordinates for the vertices of a steritruncated 5-orthoplex, centered at the origin, are all permutations of
Images
Stericantitruncated 5-orthoplex
Alternate names
Stericantitruncated pentacross
Celligreatorhombated triacontaditeron (cogart) (Jonathan Bowers)
Coordinates
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:
Images
Omnitruncated 5-cube
Alternate names
Steriruncicantitruncated 5-cube (Full expansion of omnitruncation for 5-polytopes by Johnson) Omnitruncated penteract Omnitruncated triacontiditeron / omnitruncated pentacross Great cellated penteractitriacontiditeron (Jonathan Bowers)
Coordinates
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:
Images
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 [4,3,3,3]+, 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.