User:Tomruen/Stericated 5-cubes

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.

Alternate names

 * Stericated penteract / Stericated 5-orthoplex / Stericated pentacross
 * Expanded penteract / Expanded 5-orthoplex / Expanded pentacross
 * Small cellated penteract (Acronym: scan) (Jonathan Bowers)

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


 * $$\left(\pm1,\ \pm1,\ \pm1,\ \pm1,\ \pm(1+\sqrt{2})\right)$$

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

Alternate names

 * Steritruncated penteract
 * Prismatotruncated penteract (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:


 * $$\left(\pm1,\ \pm(1+\sqrt{2}),\ \pm(1+\sqrt{2}),\ \pm(1+\sqrt{2}),\ \pm(1+2\sqrt{2})\right)$$

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:


 * $$\left(\pm1,\ \pm1,\ \pm1,\ \pm(1+\sqrt{2}),\ \pm(1+2\sqrt{2})\right)$$

Alternate names

 * Stericantitruncated penteract
 * Steriruncicantellated 16-cell / 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:


 * $$\left(1,\ 1+\sqrt{2},\ 1+2\sqrt{2},\ 1+2\sqrt{2},\ 1+3\sqrt{2}\right)$$

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:


 * $$\left(1,\ 1+\sqrt{2},\ 1+1\sqrt{2},\ 1+2\sqrt{2},\ 1+3\sqrt{2}\right)$$

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
 * $$\left(\pm1,\ \pm1,\ \pm1,\ \pm1,\ \pm(1+\sqrt{2})\right)$$

Alternate names

 * Stericantitruncated pentacross
 * Celligreatorhombated pentacross (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:


 * $$\left(1,\ 1,\ 1+\sqrt{2},\ 1+2\sqrt{2},\ 1+3\sqrt{2}\right)$$

Alternate names

 * Steriruncicantitruncated 5-cube (Full expansion of omnitruncation for 5-polytopes by Johnson)
 * Omnitruncated penteract
 * Omnitruncated 16-cell / omnitruncated pentacross
 * Great cellated penteractitriacontiditeron (Jonathan Bowers)

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


 * $$\left(1,\ 1+\sqrt{2},\ 1+2\sqrt{2},\ 1+3\sqrt{2},\ 1+4\sqrt{2}\right)$$

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