# Great cellated tesseractic tetracomb

Great cellated tesseractic tetracomb
Rank5
TypeUniform
SpaceEuclidean
Notation
Bowers style acronymGacotat
Coxeter diagramx4x3x3x4x ()
Elements
Tera3N octagonal duoprisms, 4N great rhombicuboctahedral prisms, N great disprismatotesseractihexadecachora
Cells24N cubes, 32N hexagonal prisms, 24N+24N octagonal prisms, 8N truncated octahedra, 8N great rhombicuboctahedra
Faces48N+48N+96N+96N squares, 64N hexagons, 48N octagons
Edges96N+192N+192N
Vertices192N
Vertex figurePhyllic disphenoidal pyramid, edge lengths 2 (6), 3 (2), and 2+2 (2)
Related polytopes
ArmyGacotat
RegimentGacotat
ConjugateQuasiquasicellated tesseractic tetracomb
Abstract & topological properties
OrientableYes
Properties
SymmetryR5×2
ConvexYes
NatureTame

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:

• ${\displaystyle \left(\pm {\frac {1}{2}}+(2+3{\sqrt {2}})i,\,\pm {\frac {1+{\sqrt {2}}}{2}}+(2+3{\sqrt {2}})j,\,\pm {\frac {1+2{\sqrt {2}}}{2}}+(2+3{\sqrt {2}})k,\,\pm {\frac {1+3{\sqrt {2}}}{2}}+(2+3{\sqrt {2}})l\right)}$,

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