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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...

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

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

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

order truncations of the regular 6-orthoplex. There are unique 16 degrees of pentellations of the 6-orthoplex with permutations of truncations, cantellations...

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

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

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

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...

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

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...

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

order truncations (runcination) of the regular 7-orthoplex. There are 16 unique runcinations of the 7-orthoplex with permutations of truncations, and cantellations...

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

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

spheres in 8 dimensions which forms the E 8 {\displaystyle \mathbb {E} _{8}} lattice. The 621 honeycomb is made of 9-simplexes and 9-orthoplexes, with 1023...

4-orthoplexes Generalized 4-orthoplexes have a regular construction as and quasiregular form as . All elements are simplexes. Real {3,3,4}, or , with 8...

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