seven-dimensional geometry, a cantellated 7-simplex is a convex uniform 7-polytope, being a cantellation of the regular 7-simplex. There are unique 6 degrees...

triangular prisms), and 27 4-faces (6 cantellated 5-cell, 6 rectified 5-cells, and 15 tetrahedral prisms). Cantellated hexateron Small rhombated hexateron...

(Acronym: sril) (Jonathan Bowers) The vertices of the cantellated 6-simplex can be most simply positioned in 7-space as permutations of (0,0,0,0,1,1,2). This...

In eight-dimensional geometry, a cantellated 8-simplex is a convex uniform 8-polytope, being a cantellation of the regular 8-simplex. There are six unique...

that are facets of 7-simplexes. Since every 7-orthoplex has 128 (27) 6-simplex facets, half of which are not incident to 7-simplexes, the 421 polytope has...

series in 1900 as containing all regular polytope facets, containing all simplexes and orthoplexes (equilateral triangles and squares in the case of the...

Steri-truncated 8-simplex Bisteri-truncated 8-simplex Steri-cantellated 8-simplex Bisteri-cantellated 8-simplex Stericanti-truncated 8-simplex Bistericanti-truncated...

series in 1900 as containing all regular polytope facets, containing all simplexes and orthoplexes (tetrahedrons and octahedrons in the case of the rectified...

unless it is all 5 vertices. It is impossible to rotate two concentric 4-simplexes with respect to each other such that some, but not all, of their vertices...

{3}×{3} {3}∨{3} {3,3}×{3,3} {3,3}∨{3,3} Facets {3} t{3,3} r{3,3,3} 2t{3,3,3,3} 2r{3,3,3,3,3} 3t{3,3,3,3,3,3} As intersecting dual simplexes ∩ ∩ ∩ ∩ ∩ ∩ ∩...