a cantellated 8-simplex is a convex uniform 8-polytope, being a cantellation of the regular 8-simplex. There are six unique cantellations for the 8-simplex...

eight-dimensional geometry, a stericated 8-simplex is a convex uniform 8-polytope with 4th order truncations (sterication) of the regular 8-simplex. There are 16 unique...

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

(acronym: saro) (Jonathan Bowers) The vertices of the cantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,0,1,1,2). This...

In six-dimensional geometry, a cantellated 6-simplex is a convex uniform 6-polytope, being a cantellation of the regular 6-simplex. There are unique 4...

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...

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...

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

Coxeter-Dynkin diagrams: The A7 family has symmetry of order 40320 (8 factorial). There are 71 (64+8-1) forms based on all permutations of the Coxeter-Dynkin diagrams...

Beauty of Geometry: Twelve Essays, Dover Publications, 1999, ISBN 0-486-40919-8 p. 88 (Chapter 5: Regular Skew Polyhedra in three and four dimensions and...