# Great rhombated tesseractic tetracomb

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

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:

• ${\displaystyle \left(±\frac12+(1+2\sqrt2)i,\,±\frac{1+\sqrt2}{2}+(1+2\sqrt2)j,\,±\frac{1+2\sqrt2}{2}+(1+2\sqrt2)k,\,±\frac{1+2\sqrt2}{2}+(1+2\sqrt2)l\right),}$

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

## Representations

A great rhombated tesseractic tetracomb has the following Coxeter diagrams:

• x4x3x3o4o (full symmetry)
• o3x3o *b3x4x (half symmetry)

## Related polytopes

o4o3o3o4o truncations
Name OBSA CD diagram Picture
Tesseractic tetracomb test
Rectified tesseractic tetracomb rittit
Icositetrachoric tetracomb icot
Truncated tesseractic tetracomb tattit
Bitruncated tesseractic tetracomb batitit
Small rhombated tesseractic tetracomb srittit
Rectified icositetrachoric tetracomb ricot
Great rhombated tesseractic tetracomb grittit
Truncated icositetrachoric tetracomb ticot
Small prismated tesseractic tetracomb sidpitit
Prismatotruncated tesseractic tetracomb potatit
Prismatorhombated tesseractic tetracomb prittit
Great prismated tesseractic tetracomb gippittit
Tesseractic tetracomb test
Celliprismated tesseractic tetracomb capotat
Cellirhombated tesseractic tetracomb scartit
Celligreatorhombated tesseractic tetracomb gicartit
Celliprismatotruncated tesseractic tetracomb captatit
Great cellated tesseractic tetracomb otatit