# Cantellated 5 cubes

Updated on
Covid-19

In six-dimensional geometry, a cantellated 5-cube is a convex uniform 5-polytope, being a cantellation of the regular 5-cube.

## Contents

There are 6 unique cantellation for the 5-cube, including truncations. Half of them are more easily constructed from the dual 5-orthoplex

## Alternate names

• Small rhombated penteract (Acronym: sirn) (Jonathan Bowers)
• ## Coordinates

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

( ± 1 ,   ± 1 ,   ± ( 1 + 2 ) ,   ± ( 1 + 2 ) ,   ± ( 1 + 2 ) )

## Bicantellated 5-cube

In five-dimensional geometry, a bicantellated 5-cube is a uniform 5-polytope.

## Alternate names

• Bicantellated penteract, bicantellated 5-orthoplex, or bicantellated pentacross
• Small birhombated penteractitriacontiditeron (Acronym: sibrant) (Jonathan Bowers)
• ## Coordinates

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

(0,1,1,2,2)

## Alternate names

• Tricantitruncated 5-orthoplex / tricantitruncated pentacross
• Great rhombated penteract (girn) (Jonathan Bowers)
• ## Coordinates

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

( 1 ,   1 + 2 ,   1 + 2 2 ,   1 + 2 2 ,   1 + 2 2 )

## Alternate names

• Bicantitruncated penteract
• Bicantitruncated pentacross
• Great birhombated penteractitriacontiditeron (Acronym: gibrant) (Jonathan Bowers)
• ## Coordinates

Cartesian coordinates for the vertices of a bicantitruncated 5-cube, centered at the origin, are all sign and coordinate permutations of

(±3,±3,±2,±1,0)

## Related polytopes

These polytopes are from a set of 31 uniform 5-polytopes generated from the regular 5-cube or 5-orthoplex.

## References

Cantellated 5-cubes Wikipedia

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