Great rhombated tesseractic tetracomb

Great rhombated tesseractic tetracomb
Rank	5
Type	Uniform
Space	Euclidean
Notation
Bowers style acronym	Grittit
Coxeter diagram	x4x3x3o4o ()
Elements
Tera	4N octahedral prisms, N truncated hexadecachora, N great rhombated tesseracts
Cells	32N triangular prisms, 8N octahedra, 16N truncated tetrahedra, 4N great rhombicuboctahedra
Faces	64N triangles, 48N squares, 32N hexagons, 6N octagons
Edges	24N+24N+96N
Vertices	48N
Vertex figure	Square pyramidal pyramid, edge lengths 1 (base), √2 (sides of pyramid 1), √3 (sides of pyramid 2), and √2+√2 (lacing between apices)
Related polytopes
Army	Grittit
Regiment	Grittit
Conjugate	Great quasirhombated tesseractic tetracomb
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	R5
Convex	Yes

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:

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

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)

External links

• Klitzing, Richard. "grittit".

• Wikipedia Contributors. "Cantitruncated tesseractic honeycomb".