a truncated 6-orthoplex is a convex uniform 6-polytope, being a truncation of the regular 6-orthoplex. There are 5 degrees of truncation for the 6-orthoplex...

six-dimensional geometry, a pentellated 6-orthoplex is a convex uniform 6-polytope with 5th order truncations of the regular 6-orthoplex. There are unique 16 degrees...

geometry, a stericated 6-orthoplex is a convex uniform 6-polytope, constructed as a sterication (4th order truncation) of the regular 6-orthoplex. There are...

6-orthoplex. There are 8 cantellation for the 6-orthoplex including truncations. Half of them are more easily constructed from the dual 5-cube Cantellated...

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...

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

six-dimensional geometry, a runcinated 6-orthplex is a convex uniform 6-polytope with 3rd order truncations (runcination) of the regular 6-orthoplex. There are 12 unique...

the 7-orthoplex. The final three truncations are best expressed relative to the 7-cube. Truncated heptacross Truncated hecatonicosoctaexon (Jonathan Bowers)...

some of the Johnson solids, the truncated right triangular prism, and Schönhardt polyhedron. A triangular prism has 6 vertices, 9 edges, and 5 faces....

There are ten degrees of cantellation for the 7-orthoplex, including truncations. Six are most simply constructible from the dual 7-cube. Small rhombated...

order truncations (sterication) of the regular 7-orthoplex. There are 24 unique sterication for the 7-orthoplex with permutations of truncations, cantellations...

order truncations (pentellation) of the regular 7-orthoplex. There are 32 unique pentellations of the 7-orthoplex with permutations of truncations, cantellations...

6th-order truncations (hexication) from the regular 7-orthoplex. There are 32 hexications for the 7-orthoplex, including all permutations of truncations, cantellations...

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

order truncations (runcination) of the regular 7-orthoplex. There are 16 unique runcinations of the 7-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...

vertices, and 99 facets: 27 5-orthoplexes and 72 5-simplices. Its vertex figure is a 5-demicube. For visualization this 6-dimensional polytope is often...

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

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

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

The square is the n = 2 case of the families of n-hypercubes and n-orthoplexes. The perimeter of a square whose four sides have length ℓ {\displaystyle...

generalized orthoplexes. They share vertices with the 4D q-q duopyramids, vertices connected by 2-edges. 2{4}2, , with 4 vertices, and 4 edges 2{4}3, , with 6 vertices...

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...

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 generating...

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