Runcinated 6-simplexes


In six-dimensional geometry, a runcinated 6-simplex is a convex uniform 6-polytope constructed as a runcination of the regular 6-simplex.
There are 8 unique runcinations of the 6-simplex with permutations of truncations, and cantellations.

Runcinated 6-simplex

Alternate names

Coordinates

The vertices of the runcinated 6-simplex can be most simply positioned in 7-space as permutations of. This construction is based on facets of the runcinated 7-orthoplex.

Biruncinated 6-simplex

Alternate names

  • Small biprismated tetradecapeton

Coordinates

The vertices of the biruncinated 6-simplex can be most simply positioned in 7-space as permutations of. This construction is based on facets of the biruncinated 7-orthoplex.

Runcitruncated 6-simplex

Alternate names

  • Prismatotruncated heptapeton

Coordinates

The vertices of the runcitruncated 6-simplex can be most simply positioned in 7-space as permutations of. This construction is based on facets of the runcitruncated 7-orthoplex.

Biruncitruncated 6-simplex

Alternate names

  • Biprismatorhombated heptapeton

Coordinates

The vertices of the biruncitruncated 6-simplex can be most simply positioned in 7-space as permutations of. This construction is based on facets of the biruncitruncated 7-orthoplex.

Runcicantellated 6-simplex

Alternate names

  • Prismatorhombated heptapeton

Coordinates

The vertices of the runcicantellated 6-simplex can be most simply positioned in 7-space as permutations of. This construction is based on facets of the runcicantellated 7-orthoplex.

Runcicantitruncated 6-simplex

Alternate names

  • Runcicantitruncated heptapeton
  • Great prismated heptapeton

Coordinates

The vertices of the runcicantitruncated 6-simplex can be most simply positioned in 7-space as permutations of. This construction is based on facets of the runcicantitruncated 7-orthoplex.

Biruncicantitruncated 6-simplex

Alternate names

  • Biruncicantitruncated heptapeton
  • Great biprismated tetradecapeton

Coordinates

The vertices of the biruncicantittruncated 6-simplex can be most simply positioned in 7-space as permutations of. This construction is based on facets of the biruncicantitruncated 7-orthoplex.

Related uniform 6-polytopes

The truncated 6-simplex is one of 35 uniform 6-polytopes based on the Coxeter group, all shown here in A6 Coxeter plane orthographic projections.