Rectified 7-simplexes
In seven-dimensional geometry, a rectified 7-simplex is a convex uniform 7-polytope, being a rectification of the regular 7-simplex.
There are four unique degrees of rectifications, including the zeroth, the 7-simplex itself. Vertices of the rectified 7-simplex are located at the edge-centers of the 7-simplex. Vertices of the birectified 7-simplex are located in the triangular face centers of the 7-simplex. Vertices of the trirectified 7-simplex are located in the tetrahedral cell centers of the 7-simplex.
Rectified 7-simplex
The rectified 7-simplex is the edge figure of the 2 [51 honeycomb|251 honeycomb]. It is called 05,1 for its branching Coxeter-Dynkin diagram, shown as.E. L. Elte identified it in 1912 as a semiregular polytope, labeling it as S.
Alternate names
- Rectified octaexon
Coordinates
Images
Birectified 7-simplex
identified it in 1912 as a semiregular polytope, labeling it as S. It is also called 04,2 for its branching Coxeter-Dynkin diagram, shown as.Alternate names
- Birectified octaexon
Coordinates
Images
Trirectified 7-simplex
The trirectified 7-simplex is the intersection of two regular 7-simplexes in dual configuration.E. L. Elte identified it in 1912 as a semiregular polytope, labeling it as S.
This polytope is the vertex figure of the 133 honeycomb. It is called 03,3 for its branching Coxeter-Dynkin diagram, shown as.
Alternate names
- Hexadecaexon
Coordinates
The trirectified 7-simplex is the intersection of two regular 7-simplices in dual configuration. This characterization yields simple coordinates for the vertices of a trirectified 7-simplex in 8-space: the 70 distinct permutations of.