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2. Cantellated 7-cubes - Wikipedia

   en.wikipedia.org/wiki/Cantellated_7-cubes

   Cantellated 7-cubes. In seven-dimensional geometry, a cantellated 7-cube is a convex uniform 7-polytope, being a cantellation of the regular 7-cube . There are 10 degrees of cantellation for the 7-cube, including truncations. 4 are most simply constructible from the dual 7-orthoplex .

3. Uniform 9-polytope - Wikipedia

   en.wikipedia.org/wiki/Uniform_9-polytope

   Uniform 9-polytope. In nine-dimensional geometry, a nine-dimensional polytope or 9-polytope is a polytope contained by 8-polytope facets. Each 7-polytope ridge being shared by exactly two 8-polytope facets . A uniform 9-polytope is one which is vertex-transitive, and constructed from uniform 8-polytope facets .

4. Pentellated 6-cubes - Wikipedia

   en.wikipedia.org/wiki/Pentellated_6-cubes

   The simple pentellated 6-cube is also called an expanded 6-cube, constructed by an expansion operation applied to the regular 6-cube. The highest form, the pentisteriruncicantitruncated 6-cube, is called an omnitruncated 6-cube with all of the nodes ringed. Six of them are better constructed from the 6-orthoplex given at pentellated 6-orthoplex .

5. Stericated 6-cubes - Wikipedia

   en.wikipedia.org/wiki/Stericated_6-cubes

   Stericated 6-cubes. In six-dimensional geometry, a stericated 6-cube is a convex uniform 6-polytope, constructed as a sterication (4th order truncation) of the regular 6-cube . There are 8 unique sterications for the 6-cube with permutations of truncations, cantellations, and runcinations.

6. Pentellated 7-cubes - Wikipedia

   en.wikipedia.org/wiki/Pentellated_7-cubes

   Pentellated 7-cubes. In seven-dimensional geometry, a pentellated 7-cube is a convex uniform 7-polytope with 5th order truncations ( pentellation) of the regular 7-cube. There are 32 unique pentellations of the 7-cube with permutations of truncations, cantellations, runcinations, and sterications. 16 are more simply constructed relative to the ...

7. Rectified 8-orthoplexes - Wikipedia

   en.wikipedia.org/wiki/Rectified_8-orthoplexes

   Rectified 8-orthoplexes. In eight-dimensional geometry, a rectified 8-orthoplex is a convex uniform 8-polytope, being a rectification of the regular 8-orthoplex . There are unique 8 degrees of rectifications, the zeroth being the 8-orthoplex, and the 7th and last being the 8-cube. Vertices of the rectified 8-orthoplex are located at the edge ...