# 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

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:

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

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

## 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