Truncated 7-orthoplexes


In seven-dimensional geometry, a truncated 7-orthoplex is a convex uniform 7-polytope, being a truncation of the regular 7-orthoplex.
There are 6 truncations of the 7-orthoplex. Vertices of the truncation 7-orthoplex are located as pairs on the edge of the 7-orthoplex. Vertices of the bitruncated 7-orthoplex are located on the triangular faces of the 7-orthoplex. Vertices of the tritruncated 7-orthoplex are located inside the tetrahedral cells of the 7-orthoplex. The final three truncations are best expressed relative to the 7-cube.

Truncated 7-orthoplex

Alternate names

Coordinates

Cartesian coordinates for the vertices of a truncated 7-orthoplex, centered at the origin, are all 168 vertices are sign and coordinate permutations of

Construction

There are two Coxeter groups associated with the truncated 7-orthoplex, one with the C7 or Coxeter group, and a lower symmetry with the D7 or Coxeter group.

Bitruncated 7-orthoplex

Alternate names

  • Bitruncated heptacross
  • Bitruncated hecatonicosoctaexon

Coordinates

Cartesian coordinates for the vertices of a bitruncated 7-orthoplex, centered at the origin, are all sign and coordinate permutations of

Tritruncated 7-orthoplex

The tritruncated 7-orthoplex can tessellation space in the quadritruncated 7-cubic honeycomb.

Alternate names

  • Tritruncated heptacross
  • Tritruncated hecatonicosoctaexon

Coordinates

Cartesian coordinates for the vertices of a tritruncated 7-orthoplex, centered at the origin, are all sign and coordinate permutations of