Pentellated 7-orthoplexes

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In seven-dimensional space, a pentellated 7-orthoplex is a uniform 7-polytope formed by fifth-order truncations of the regular 7-orthoplex. There are 32 distinct pentellations, created by different combinations of truncation operations (pentellation, cantellation, runcination, and sterication). Of these, 16 can be obtained more simply from the 7-cube. This family is part of the 127 uniform 7-polytopes with B7 symmetry.

The vertices can be described as all permutations of several base vectors (some scaled by √2). The 16 coordinate families are:
- (0,1,1,1,1,1,2)√2
- (0,1,1,1,1,2,3)
- (0,1,1,1,2,2,3)√2
- (0,1,1,1,2,3,4)√2
- (0,1,1,2,2,2,3)√2
- (0,1,1,2,2,3,4)√2
- (0,1,1,2,3,3,4)√2
- (0,1,1,2,3,4,5)√2
- (0,1,2,2,2,2,3)√2
- (0,1,2,2,2,3,4)√2
- (0,1,2,2,3,3,4)√2
- (0,1,2,2,3,4,5)√2
- (0,1,2,3,3,3,4)√2
- (0,1,2,3,3,4,5)√2
- (0,1,2,3,4,4,5)√2
- (0,1,2,3,4,5,6)√2

These patterns define the vertex coordinates for the pentellated 7-orthoplexes.