Rectified 10-simplexes

In ten-dimensional geometry, a rectified 10-simplex is a convex uniform 10-polytope, being a rectification of the regular 10-simplex.

These polytopes are part of a family of 527 uniform 10-polytopes with A10 symmetry.

There are unique 5 degrees of rectifications including the zeroth, the 10-simplex itself. Vertices of the rectified 10-simplex are located at the edge-centers of the 10-simplex. Vertices of the birectified 10-simplex are located in the triangular face centers of the 10-simplex. Vertices of the trirectified 10-simplex are located in the tetrahedral cell centers of the 10-simplex. Vertices of the quadrirectified 10-simplex are located in the 5-cell centers of the 10-simplex.

Rectified 10-simplex
The rectified 10-simplex is the vertex figure of the 11-demicube.

Alternate names

 * Rectified hendecaxennon (Acronym ru) (Jonathan Bowers)

Coordinates
The Cartesian coordinates of the vertices of the rectified 10-simplex can be most simply positioned in 11-space as permutations of (0,0,0,0,0,0,0,0,0,1,1). This construction is based on facets of the rectified 11-orthoplex.

Alternate names

 * Birectified hendecaxennon (Acronym bru) (Jonathan Bowers)

Coordinates
The Cartesian coordinates of the vertices of the birectified 10-simplex can be most simply positioned in 11-space as permutations of (0,0,0,0,0,0,0,0,1,1,1). This construction is based on facets of the birectified 11-orthoplex.

Alternate names

 * Trirectified hendecaxennon (Jonathan Bowers)

Coordinates
The Cartesian coordinates of the vertices of the trirectified 10-simplex can be most simply positioned in 11-space as permutations of (0,0,0,0,0,0,0,1,1,1,1). This construction is based on facets of the trirectified 11-orthoplex.

Alternate names

 * Quadrirectified hendecaxennon (Acronym teru) (Jonathan Bowers)

Coordinates
The Cartesian coordinates of the vertices of the quadrirectified 10-simplex can be most simply positioned in 11-space as permutations of (0,0,0,0,0,0,1,1,1,1,1). This construction is based on facets of the quadrirectified 11-orthoplex.