# Great rhombated tesseractic tetracomb

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Great rhombated tesseractic tetracomb
Rank5
TypeUniform
SpaceEuclidean
Notation
Bowers style acronymGrittit
Coxeter diagramx4x3x3o4o ()
Elements
Tera4N octahedral prisms, N truncated hexadecachora, N great rhombated tesseracts
Cells32N triangular prisms, 8N octahedra, 16N truncated tetrahedra, 4N great rhombicuboctahedra
Faces64N triangles, 48N squares, 32N hexagons, 6N octagons
Edges24N+24N+96N
Vertices48N
Vertex figureSquare pyramidal pyramid, edge lengths 1 (base), 2 (sides of pyramid 1), 3 (sides of pyramid 2), and 2+2 (lacing between apices)
Related polytopes
ArmyGrittit
RegimentGrittit
ConjugateGreat quasirhombated tesseractic tetracomb
Abstract & topological properties
OrientableYes
Properties
SymmetryR5
ConvexYes
NatureTame

The great rhombated tesseractic tetracomb or grittit, also called the cantitruncated tesseractic tetracomb, is a convex uniform tetracomb. 4 great rhombated tesseracts, 1 truncated hexadecachoron, and 1 octahedral prism join at each vertex of this tessellation. As the name suggests, it is the cantitruncation of the tesseractic tetracomb.

## Vertex coordinates

The vertices of a great rhombated tesseractic tetracomb of edge length 1 are given by all permutations of:

• ${\displaystyle \left(\pm {\frac {1}{2}}+(1+2{\sqrt {2}})i,\,\pm {\frac {1+{\sqrt {2}}}{2}}+(1+2{\sqrt {2}})j,\,\pm {\frac {1+2{\sqrt {2}}}{2}}+(1+2{\sqrt {2}})k,\,\pm {\frac {1+2{\sqrt {2}}}{2}}+(1+2{\sqrt {2}})l\right)}$,

where i , j , k , and l  range over the integers.

## Representations

A great rhombated tesseractic tetracomb has the following Coxeter diagrams:

• x4x3x3o4o () (full symmetry)
• o3x3x4x *b3o () (half symmetry)