In ten-dimensional geometry, a rectified 10-orthoplex is a convex uniform 10-polytope, being a rectification of the regular 10-orthoplex.
There are 10 rectifications of the 10-orthoplex. Vertices of the rectified 10-orthoplex are located at the edge-centers of the 9-orthoplex. Vertices of the birectified 10-orthoplex are located in the triangular face centers of the 10-orthoplex. Vertices of the trirectified 10-orthoplex are located in the tetrahedral cell centers of the 10-orthoplex.
These polytopes are part of a family of 1023 uniform 10-polytopes with BC<sub>10</sub> symmetry.
In ten-dimensional geometry, a rectified 10-orthoplex is a 10-polytope, being a rectification of the regular 10-orthoplex.
The rectified 10-orthoplex is the vertex figure of the demidekeractic honeycomb.
There are two Coxeter groups associated with the rectified 10-orthoplex, one with the C<sub>10</sub> or [4,3<sup>8</sup>] Coxeter group, and a lower symmetry with two copies of 9-orthoplex facets, alternating, with the D<sub>10</sub> or [3<sup>7,1,1</sup>] Coxeter group.
Cartesian coordinates for the vertices of a rectified 10-orthoplex, centered at the origin, edge length are all permutations of:
Its 180 vertices represent the root vectors of the simple Lie group D<sub>10</sub>. The vertices can be seen in 3 hyperplanes, with the 45 vertices rectified 9-simplices facets on opposite sides, and 90 vertices of an expanded 9-simplex passing through the center. When combined with the 20 vertices of the 9-orthoplex, these vertices represent the 200 root vectors of the simple Lie group B<sub>10</sub>.
Cartesian coordinates for the vertices of a birectified 10-orthoplex, centered at the origin, edge length are all permutations of:
Cartesian coordinates for the vertices of a trirectified 10-orthoplex, centered at the origin, edge length are all permutations of:
Cartesian coordinates for the vertices of a quadrirectified 10-orthoplex, centered at the origin, edge length are all permutations of: