Wikipedia / 9-simplex
Wikipedia / 9-simplex
In geometry, a 9-simplex is a self-dual regular 9-polytope. It has 10 vertices, 45 edgess, 120 triangle faces, 210 tetrahedral cells, 252 5-cell 4-faces, 210 5-simplex 5-faces, 120 6-simplex 6-faces, 45 7-simplex 7-faces, and 10 8-simplex 8-faces. Its dihedral angle is cos−1(1/9), or approximately 83.62°.
It can also be called a decayotton, or deca-9-tope, as a 10-facetted polytope in 9-dimensions. The name decayotton is derived from deca for ten facets in Greek and yotta (a variation of "oct" for eight), having 8-dimensional facets, and -on. Jonathan Bowers gives it acronym day.
Coordinates
The Cartesian coordinates of the vertices of an origin-centered regular decayotton having edge length2 are:
More simply, the vertices of the 9-simplex can be positioned in 10-space as permutations of (0,0,0,0,0,0,0,0,0,1). These are the vertices of one facet of the 10-orthoplex.
Images
References
(Paper 22)
(Paper 23)
(Paper 24)