Hexicated 7-simplexes
In seven-dimensional geometry, a hexicated 7-simplex is a convex uniform 7-polytope, including 6th-order truncations from the regular 7-simplex.
There are 20 unique hexications for the 7-simplex, including all permutations of truncations, cantellations, runcinations, sterications, and pentellations.
The simple hexicated 7-simplex is also called an expanded 7-simplex, with only the first and last nodes ringed, is constructed by an expansion operation applied to the regular 7-simplex. The highest form, the hexipentisteriruncicantitruncated 7-simplex is more simply called an omnitruncated 7-simplex with all of the nodes ringed.
Hexicated 7-simplex
In seven-dimensional geometry, a hexicated 7-simplex is a convex uniform 7-polytope, a hexication of the regular 7-simplex, or alternately can be seen as an expansion operation.Root vectors
Its 56 vertices represent the root vectors of the simple Lie group A7.Alternate names
- Expanded 7-simplex
- Small petated hexadecaexon
Coordinates
The vertices of the hexicated 7-simplex can be most simply positioned in 8-space as permutations of. This construction is based on facets of the hexicated 8-orthoplex,.A second construction in 8-space, from the center of a rectified 8-orthoplex is given by coordinate permutations of:
Hexitruncated 7-simplex
Alternate names
- Petitruncated octaexon
Coordinates
The vertices of the hexitruncated 7-simplex can be most simply positioned in 8-space as permutations of. This construction is based on facets of the hexitruncated 8-orthoplex,.Hexicantellated 7-simplex
Alternate names
- Petirhombated octaexon
Coordinates
The vertices of the hexicantellated 7-simplex can be most simply positioned in 8-space as permutations of. This construction is based on facets of the hexicantellated 8-orthoplex,.Hexiruncinated 7-simplex
Alternate names
- Petaprismated hexadecaexon
Coordinates
The vertices of the hexiruncinated 7-simplex can be most simply positioned in 8-space as permutations of. This construction is based on facets of the hexiruncinated 8-orthoplex,.Hexicantitruncated 7-simplex
Alternate names
- Petigreatorhombated octaexon
Coordinates
The vertices of the hexicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of. This construction is based on facets of the hexicantitruncated 8-orthoplex,.Hexiruncitruncated 7-simplex
Alternate names
- Petiprismatotruncated octaexon
Coordinates
The vertices of the hexiruncitruncated 7-simplex can be most simply positioned in 8-space as permutations of. This construction is based on facets of the hexiruncitruncated 8-orthoplex,.Hexiruncicantellated 7-simplex
In seven-dimensional geometry, a hexiruncicantellated 7-simplex is a uniform 7-polytope.Alternate names
- Petiprismatorhombated octaexon
Coordinates
The vertices of the hexiruncicantellated 7-simplex can be most simply positioned in 8-space as permutations of. This construction is based on facets of the hexiruncicantellated 8-orthoplex,.Hexisteritruncated 7-simplex
Alternate names
- Peticellitruncated octaexon
Coordinates
The vertices of the hexisteritruncated 7-simplex can be most simply positioned in 8-space as permutations of. This construction is based on facets of the hexisteritruncated 8-orthoplex,.Hexistericantellated 7-simplex
Alternate names
- Peticellirhombihexadecaexon
Coordinates
The vertices of the hexistericantellated 7-simplex can be most simply positioned in 8-space as permutations of. This construction is based on facets of the hexistericantellated 8-orthoplex,.Hexipentitruncated 7-simplex
Alternate names
- Petiteritruncated hexadecaexon
Coordinates
The vertices of the hexipentitruncated 7-simplex can be most simply positioned in 8-space as permutations of. This construction is based on facets of the hexipentitruncated 8-orthoplex,.Hexiruncicantitruncated 7-simplex
Alternate names
- Petigreatoprismated octaexon
Coordinates
The vertices of the hexiruncicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of. This construction is based on facets of the hexiruncicantitruncated 8-orthoplex,.Hexistericantitruncated 7-simplex
Alternate names
- Peticelligreatorhombated octaexon
Coordinates
The vertices of the hexistericantitruncated 7-simplex can be most simply positioned in 8-space as permutations of. This construction is based on facets of the hexistericantitruncated 8-orthoplex,.Hexisteriruncitruncated 7-simplex
Alternate names
- Peticelliprismatotruncated octaexon
Coordinates
The vertices of the hexisteriruncitruncated 7-simplex can be most simply positioned in 8-space as permutations of. This construction is based on facets of the hexisteriruncitruncated 8-orthoplex,.Hexisteriruncicantellated 7-simplex
Alternate names
- Peticelliprismatorhombihexadecaexon
Coordinates
The vertices of the hexisteriruncitruncated 7-simplex can be most simply positioned in 8-space as permutations of. This construction is based on facets of the hexisteriruncitruncated 8-orthoplex,.Hexipenticantitruncated 7-simplex
Alternate names
- Petiterigreatorhombated octaexon
Coordinates
The vertices of the hexipenticantitruncated 7-simplex can be most simply positioned in 8-space as permutations of. This construction is based on facets of the hexipenticantitruncated 8-orthoplex,.Hexipentiruncitruncated 7-simplex
Alternate names
- Petiteriprismatotruncated hexadecaexon
Coordinates
The vertices of the hexipentiruncitruncated 7-simplex can be most simply positioned in 8-space as permutations of. This construction is based on facets of the hexipentiruncitruncated 8-orthoplex,.Hexisteriruncicantitruncated 7-simplex
Alternate names
- Petigreatocellated octaexon
Coordinates
The vertices of the hexisteriruncicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of. This construction is based on facets of the hexisteriruncicantitruncated 8-orthoplex,.Hexipentiruncicantitruncated 7-simplex
Alternate names
- Petiterigreatoprismated octaexon
Coordinates
The vertices of the hexipentiruncicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of. This construction is based on facets of the hexipentiruncicantitruncated 8-orthoplex,.Hexipentistericantitruncated 7-simplex
Alternate names
- Petitericelligreatorhombihexadecaexon
Coordinates
The vertices of the hexipentistericantitruncated 7-simplex can be most simply positioned in 8-space as permutations of. This construction is based on facets of the hexipentistericantitruncated 8-orthoplex,.Omnitruncated 7-simplex
The omnitruncated 7-simplex is composed of 40320 vertices and is the largest uniform 7-polytope in the A7 symmetry of the regular 7-simplex. It can also be called the hexipentisteriruncicantitruncated 7-simplex which is the long name for the omnitruncation for 7 dimensions, with all reflective mirrors active.Permutohedron and related tessellation
The omnitruncated 7-simplex is the permutohedron of order 8. The omnitruncated 7-simplex is a zonotope, the Minkowski sum of eight line segments parallel to the eight lines through the origin and the eight vertices of the 7-simplex.Like all uniform omnitruncated n-simplices, the omnitruncated 7-simplex can tessellate space by itself, in this case 7-dimensional space with three facets around each ridge. It has Coxeter-Dynkin diagram of.
Alternate names
- Great petated hexadecaexon