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In eight-dimensional geometry, a truncated 8-simplex is a convex uniform 8-polytope, being a truncation of the regular 8-simplex.
Contents
There are a four unique degrees of truncation. Vertices of the truncation 8-simplex are located as pairs on the edge of the 8-simplex. Vertices of the bitruncated 8-simplex are located on the triangular faces of the 8-simplex. Vertices of the tritruncated 8-simplex are located inside the tetrahedral cells of the 8-simplex.
Alternate names
Coordinates
The Cartesian coordinates of the vertices of the truncated 8-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,0,0,0,1,2). This construction is based on facets of the truncated 9-orthoplex.
Alternate names
Coordinates
The Cartesian coordinates of the vertices of the bitruncated 8-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,0,0,1,2,2). This construction is based on facets of the bitruncated 9-orthoplex.
Alternate names
Coordinates
The Cartesian coordinates of the vertices of the tritruncated 8-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,0,1,2,2,2). This construction is based on facets of the tritruncated 9-orthoplex.
Quadritruncated 8-simplex
The quadritruncated 8-simplex an isotopic polytope, constructed from 18 tritruncated 7-simplex facets.
Alternate names
Coordinates
The Cartesian coordinates of the vertices of the quadritruncated 8-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,1,2,2,2,2). This construction is based on facets of the quadritruncated 9-orthoplex.
Related polytopes
This polytope is one of 135 uniform 8-polytopes with A8 symmetry.