Rectified 10-orthoplexes
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 BC10 symmetry.
Rectified 10-orthoplex
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.
Alternate names
- Rectified decacross
Construction
There are two Coxeter groups associated with the rectified 10-orthoplex, one with the C10 or Coxeter group, and a lower symmetry with two copies of 9-orthoplex facets, alternating, with the D10 or Coxeter group.Cartesian coordinates
Cartesian coordinates for the vertices of a rectified 10-orthoplex, centered at the origin, edge length are all permutations of:Root vectors
Its 180 vertices represent the root vectors of the simple Lie group D10. 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 B10.Birectified 10-orthoplex
Alternate names
- Birectified decacross
Cartesian coordinates
Cartesian coordinates for the vertices of a birectified 10-orthoplex, centered at the origin, edge length are all permutations of:Trirectified 10-orthoplex
Alternate names
- Trirectified decacross
Cartesian coordinates
Cartesian coordinates for the vertices of a trirectified 10-orthoplex, centered at the origin, edge length are all permutations of:Quadrirectified 10-orthoplex
Alternate names
- Quadrirectified decacross