Cantellated 8-simplexes


In eight-dimensional geometry, a cantellated 8-simplex is a convex uniform 8-polytope, being a cantellation of the regular 8-simplex.
There are six unique cantellations for the 8-simplex, including permutations of truncation.

Cantellated 8-simplex

Alternate names

Coordinates

The Cartesian coordinates of the vertices of the cantellated 8-simplex can be most simply positioned in 9-space as permutations of. This construction is based on facets of the cantellated 9-orthoplex.

Bicantellated 8-simplex

Alternate names

  • Small birhombated enneazetton

Coordinates

The Cartesian coordinates of the vertices of the bicantellated 8-simplex can be most simply positioned in 9-space as permutations of. This construction is based on facets of the bicantellated 9-orthoplex.

Tricantellated 8-simplex

Alternate names

  • Small trirhombihexadecaexon

Coordinates

The Cartesian coordinates of the vertices of the tricantellated 8-simplex can be most simply positioned in 9-space as permutations of. This construction is based on facets of the tricantellated 9-orthoplex.

Cantitruncated 8-simplex

Alternate names

  • Great rhombated enneazetton

Coordinates

The Cartesian coordinates of the vertices of the cantitruncated 8-simplex can be most simply positioned in 9-space as permutations of. This construction is based on facets of the bicantitruncated 9-orthoplex.

Bicantitruncated 8-simplex

Alternate names

  • Great birhombated enneazetton

Coordinates

The Cartesian coordinates of the vertices of the bicantitruncated 8-simplex can be most simply positioned in 9-space as permutations of. This construction is based on facets of the bicantitruncated 9-orthoplex.

Tricantitruncated 8-simplex

  • Great trirhombated enneazetton

Coordinates

The Cartesian coordinates of the vertices of the tricantitruncated 8-simplex can be most simply positioned in 9-space as permutations of. This construction is based on facets of the bicantitruncated 9-orthoplex.

Related polytopes

The six presented polytopes are in the family of 135 uniform 8-polytopes with A8 symmetry.