f5 = 7, f4 = 21, C = 35, F = 35, E = 21, V = 7 (χ=0) In geometry, a 6-simplex is a self-dual regular 6-polytope.
It has 7 vertices, 21 edges, 35 triangle faces, 35 tetrahedral cells, 21 5-cell 4-faces, and 7 5-simplex 5-faces.
Its dihedral angle is cos−1(1/6), or approximately 80.41°.
Jonathan Bowers gives a heptapeton the acronym hop.
[2] This configuration matrix represents the 6-simplex.
The rows and columns correspond to vertices, edges, faces, cells, 4-faces and 5-faces.
The diagonal numbers say how many of each element occur in the whole 6-simplex.
This self-dual simplex's matrix is identical to its 180 degree rotation.
The Cartesian coordinates for an origin-centered regular heptapeton having edge length 2 are: The vertices of the 6-simplex can be more simply positioned in 7-space as permutations of: This construction is based on facets of the 7-orthoplex.
The regular 6-simplex is one of 35 uniform 6-polytopes based on the [3,3,3,3,3] Coxeter group, all shown here in A6 Coxeter plane orthographic projections.