In six-dimensional geometry, a pentellated 6-simplex is a convexuniform 6-polytope with 5th ordertruncations 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 nodesringed.
Pentellated 6-simplex
Alternate names
Expanded 6-simplex
Small terated tetradecapeton
Coordinates
The vertices of the pentellated 6-simplex can be positioned in 7-space as permutations of. This construction is based on facets of the pentellated 7-orthoplex. A second construction in 7-space, from the center of a rectified 7-orthoplex is given by coordinate permutations of:
The vertices of the runcitruncated 6-simplex can be most simply positioned in 7-space as permutations of. This construction is based on facets of the runcitruncated 7-orthoplex.
Images
Penticantellated 6-simplex
Alternate names
Teriprismated heptapeton
Coordinates
The vertices of the runcicantellated 6-simplex can be most simply positioned in 7-space as permutations of. This construction is based on facets of the penticantellated 7-orthoplex.
Images
Penticantitruncated 6-simplex
Alternate names
Terigreatorhombated heptapeton
Coordinates
The vertices of the penticantitruncated 6-simplex can be most simply positioned in 7-space as permutations of. This construction is based on facets of the penticantitruncated 7-orthoplex.
Images
Pentiruncitruncated 6-simplex
Alternate names
Tericellirhombated heptapeton
Coordinates
The vertices of the pentiruncitruncated 6-simplex can be most simply positioned in 7-space as permutations of. This construction is based on facets of the pentiruncitruncated 7-orthoplex.
Images
Pentiruncicantellated 6-simplex
Alternate names
Teriprismatorhombated tetradecapeton
Coordinates
The vertices of the pentiruncicantellated 6-simplex can be most simply positioned in 7-space as permutations of. This construction is based on facets of the pentiruncicantellated 7-orthoplex.
Images
Pentiruncicantitruncated 6-simplex
Alternate names
Terigreatoprismated heptapeton
Coordinates
The vertices of the pentiruncicantitruncated 6-simplex can be most simply positioned in 7-space as permutations of. This construction is based on facets of the pentiruncicantitruncated 7-orthoplex.
Images
Pentisteritruncated 6-simplex
Alternate names
Tericellitruncated tetradecapeton
Coordinates
The vertices of the pentisteritruncated 6-simplex can be most simply positioned in 7-space as permutations of. This construction is based on facets of the pentisteritruncated 7-orthoplex.
Images
Pentistericantitruncated 6-simplex
Alternate names
Great teracellirhombated heptapeton
Coordinates
The vertices of the pentistericantittruncated 6-simplex can be most simply positioned in 7-space as permutations of. This construction is based on facets of the pentistericantitruncated 7-orthoplex.
The omnitruncated 6-simplex has 5040 vertices, 15120 edges,16800 faces, 8400 cells, 1806 4-faces, and 126 5-faces. With 5040 vertices, it is the largest of 35 uniform 6-polytopes generated from the regular 6-simplex.
The vertices of the omnitruncated 6-simplex can be most simply positioned in 7-space as permutations of. This construction is based on facets of the pentisteriruncicantitruncated 7-orthoplex, t0,1,2,3,4,5,.
The full snub 6-simplex or omnisnub 6-simplex, defined as an alternation of the omnitruncated 6-simplex is not uniform, but it can be given Coxeter diagram and symmetry+, and constructed from 14 snub 5-simplexes, 42 snub 5-cellantiprisms, 70 3-s duoantiprisms, and 2520 irregular 5-simplexes filling the gaps at the deleted vertices.
