Great cellated tesseractic tetracomb

Great cellated tesseractic tetracomb
Rank	5
Type	Uniform
Space	Euclidean
Notation
Bowers style acronym	Gacotat
Coxeter diagram	x4x3x3x4x ()
Elements
Tera	3N octagonal duoprisms, 4N great rhombicuboctahedral prisms, N great disprismatotesseractihexadecachora
Cells	24N cubes, 32N hexagonal prisms, 24N+24N octagonal prisms, 8N truncated octahedra, 8N great rhombicuboctahedra
Faces	48N+48N+96N+96N squares, 64N hexagons, 48N octagons
Edges	96N+192N+192N
Vertices	192N
Vertex figure	Phyllic disphenoidal pyramid, edge lengths √2 (6), √3 (2), and √2+√2 (2)
Related polytopes
Army	Gacotat
Regiment	Gacotat
Conjugate	Quasiquasicellated tesseractic tetracomb
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	R5×2
Convex	Yes

The great cellated tesseractic tetracomb or gacotat, also called the omnitruncated tesseractic tetracomb is a convex uniform tetracomb. 2 great disprismatotesseractihexadecachora, 2 great rhombicuboctahedral prisms, and 1 octagonal duoprism join at each vertex of this tessellation. As the name suggests, it is the omnitruncation of the tesseractic tetracomb.

Vertex coordinates

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

• $\left(±\frac12+(2+3\sqrt2)i,\,±\frac{1+\sqrt2}{2}+(2+3\sqrt2)j,\,±\frac{1+2\sqrt2}{2}+(2+3\sqrt2)k,\,±\frac{1+3\sqrt2}{2}+(2+3\sqrt2)l\right),$

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

External links

• Klitzing, Richard. "gacotat".

• Wikipedia Contributors. "Omnitruncated tesseractic honeycomb".