Runcinated enneazetton Small prismated enneazetton (Acronym: spene) (Jonathan Bowers) The Cartesian coordinates of the vertices of the runcinated 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...

geometry, a runcinated 7-simplex is a convex uniform 7-polytope with 3rd order truncations (runcination) of the regular 7-simplex. There are 8 unique runcinations...

and cantellations. Runcinated hexateron Small prismated hexateron (Acronym: spix) (Jonathan Bowers) The vertices of the runcinated 5-simplex can be most...

a runcinated 6-simplex is a convex uniform 6-polytope constructed as a runcination (3rd order truncations) of the regular 6-simplex. There are 8 unique...

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

cross-section of the stericated hexateron with a 4-dimensional hyperplane is a runcinated 5-cell. This cross-section divides the stericated hexateron into two pentachoral...

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...

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...

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

polyhedron, {4,6|3}, is similarly related to the square faces of the runcinated 5-cell. The disphenoidal 30-cell is the dual of the bitruncated 5-cell...