geometry, a truncated 7-orthoplex is a convex uniform 7-polytope, being a truncation of the regular 7-orthoplex. There are 6 truncations of the 7-orthoplex...

seven-dimensional geometry, a runcinated 7-orthoplex is a convex uniform 7-polytope with 3rd order truncations (runcination) of the regular 7-orthoplex. There are 16 unique...

cantellation for the 7-orthoplex, including truncations. Six are most simply constructible from the dual 7-cube. Small rhombated hecatonicosoctaexon (acronym:...

hexicated 7-orthoplex (also hexicated 7-cube) is a convex uniform 7-polytope, including 6th-order truncations (hexication) from the regular 7-orthoplex...

seven-dimensional geometry, a stericated 7-orthoplex is a convex uniform 7-polytope with 4th order truncations (sterication) of the regular 7-orthoplex. There are 24 unique...

third and fourth truncations are more easily constructed as second and first truncations of the 5-cube. Truncated pentacross Truncated triacontaditeron...

6-orthoplex. Truncated hexacross Truncated hexacontatetrapeton (Acronym: tag) (Jonathan Bowers) There are two Coxeter groups associated with the truncated hexacross...

geometry, a pentellated 7-orthoplex is a convex uniform 7-polytope with 5th order truncations (pentellation) of the regular 7-orthoplex. There are 32...

geometry, a truncated 8-orthoplex is a convex uniform 8-polytope, being a truncation of the regular 8-orthoplex. There are 7 truncation for the 8-orthoplex...

Coxeter-Dynkin diagram: . The 221 has 27 vertices, and 99 facets: 27 5-orthoplexes and 72 5-simplices. Its vertex figure is a 5-demicube. For visualization...

(4th order truncation) of the regular 6-orthoplex. There are 16 unique sterications for the 6-orthoplex with permutations of truncations, cantellations...

containing all regular polytope facets, containing all simplexes and orthoplexes (equilateral triangles and squares in the case of the triangular prism)...

infinite family of polytopes, called cross-polytopes or orthoplexes. The dual polytope is the 7-hypercube, or hepteract. Heptacross, derived from combining...

5-orthoplex. There are 6 cantellation for the 5-orthoplex, including truncations. Some of them are more easily constructed from the dual 5-cube. Cantellated...

3rd order truncation (runcination) of the regular 5-orthoplex. There are 8 runcinations of the 5-orthoplex with permutations of truncations, and cantellations...

2160 3{3}3 faces, and 240 3{3}3{3}3 cells Generalized 4-orthoplexes Generalized 4-orthoplexes have a regular construction as and quasiregular form as...

facets. The vertex figure for honeycombs of this family are rectified orthoplexes. These are also named as hδn for an (n−1)-dimensional honeycomb. Regular...

order truncations (runcination) of the regular 6-orthoplex. There are 12 unique runcinations of the 6-orthoplex with permutations of truncations, and cantellations...

hemi-cube and hemi-octahedron generalize as hemi-n-cubes and hemi-n-orthoplexes to any rank. 5 of 6 convex regular 4-polytopes are centrally symmetric...

containing all regular polytope facets, containing all simplexes and orthoplexes (tetrahedrons and octahedrons in the case of the rectified 5-cell). The...

6-orthoplex. There are 8 cantellation for the 6-orthoplex including truncations. Half of them are more easily constructed from the dual 6-cube Cantellated...

There are 12 unique uniform honeycombs, including: 5-simplex honeycomb Truncated 5-simplex honeycomb Omnitruncated 5-simplex honeycomb C ~ 5 {\displaystyle...

plane alongside other regular polygons, as with the truncated hexagonal tiling or the truncated trihexagonal tiling. A regular dodecahedron has twelve...

Complex polygons 2{r}q Polygons of the form 2{4}q are called generalized orthoplexes. They share vertices with the 4D q-q duopyramids, vertices connected...