Rectified 10-cubes

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

There are 10 rectifications of the 10-cube, with the zeroth being the 10-cube itself. Vertices of the rectified 10-cube are located at the edge-centers of the 10-cube. Vertices of the birectified 10-cube are located in the square face centers of the 10-cube. Vertices of the trirectified 10-cube are located in the cubic cell centers of the 10-cube. The others are more simply constructed relative to the 10-cube dual polytope, the 10-orthoplex.

These polytopes are part of a family 1023 uniform 10-polytopes with BC10 symmetry.

Alternate names

 * Rectified dekeract (Acronym rade) (Jonathan Bowers)

Cartesian coordinates
Cartesian coordinates for the vertices of a rectified 10-cube, centered at the origin, edge length $$\sqrt{2}$$ are all permutations of:
 * (±1,±1,±1,±1,±1,±1,±1,±1,±1,0)

Alternate names

 * Birectified dekeract (Acronym brade) (Jonathan Bowers)

Cartesian coordinates
Cartesian coordinates for the vertices of a birectified 10-cube, centered at the origin, edge length $$\sqrt{2}$$ are all permutations of:
 * (±1,±1,±1,±1,±1,±1,±1,±1,0,0)

Alternate names

 * Tririrectified dekeract (Acronym trade) (Jonathan Bowers)

Cartesian coordinates
Cartesian coordinates for the vertices of a triirectified 10-cube, centered at the origin, edge length $$\sqrt{2}$$ are all permutations of:
 * (±1,±1,±1,±1,±1,±1,±1,0,0,0)

Alternate names

 * Quadrirectified dekeract
 * Quadrirectified decacross (Acronym terade) (Jonathan Bowers)

Cartesian coordinates
Cartesian coordinates for the vertices of a quadrirectified 10-cube, centered at the origin, edge length $$\sqrt{2}$$ are all permutations of:
 * (±1,±1,±1,±1,±1,±1,0,0,0,0)