In six-dimensional geometry, a pentellated 6-simplex is a convex uniform 6-polytope with 5th order truncations of the regular 6-simplex.
There are unique 10 degrees of pentellations of the 6-simplex with permutations of truncations, cantellations, runcinations, and sterications.
The simple pentellated 6-simplex is also called an expanded 6-simplex, constructed by an expansion operation applied to the regular 6-simplex.
The highest form, the pentisteriruncicantitruncated 6-simplex, is called an omnitruncated 6-simplex with all of the nodes ringed.
This cross-section divides the pentellated 6-simplex into two hexateral hypercupolas consisting of 7 5-simplexes, 21 5-cell prisms and 35 Tetrahedral-Triangular duoprisms each.
A second construction in 7-space, from the center of a rectified 7-orthoplex is given by coordinate permutations of: Its 42 vertices represent the root vectors of the simple Lie group A6.
The rows and columns correspond to vertices, edges, faces, cells, 4-faces and 5-faces.
The rows and columns correspond to vertices, edges, faces, cells, 4-faces and 5-faces.