# Great prismated tesseractic tetracomb

The great prismated tesseractic tetracomb or gippittit, aslo called the runcicantitruncated tesseractic tetracomb, is a convex uniform tetracomb. 2 great disprismatotesseractihexadecachora, 1 truncated icositetrachoron, 1 truncated octahedral prism, and 1 square-octagonal duoprism join at each vertex of this tessellation. As the name suggests, it is the runcicantitruncation of the tesseractic tetracomb.

Great prismated tesseractic tetracomb
Rank5
TypeUniform
SpaceEuclidean
Notation
Bowers style acronymGippittit
Coxeter diagramx4x3x3x4o ()
Elements
Tera6N square-octagonal duoprisms, 4N truncated octahedral prisms, N truncated icositetrachora, N great disprismatotesseractihexadecachora
Cells24N+24N cubes, 32N hexagonal prisms, 24N octagonal prisms, 8N+16N truncated octahedra, 4N great rhombicuboctahedra
Faces48N+48N+96N+96N squares, 32N+64N hexagons, 24N octagons
Edges96N+96N+96N+192N
Vertices192N
Vertex figureSphenoidal pyramid, edge lengths 2 (6), 3 (3), 2+2 (1)
Related polytopes
ArmyGippittit
RegimentGippittit
ConjugateGreat quasiprismated tesseractic tetracomb
Abstract & topological properties
OrientableYes
Properties
SymmetryR5
ConvexYes
NatureTame

## Vertex coordinates

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

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

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

## Representations

A great prismated tesseractic tetracomb has the following Coxeter diagrams:

• x4x3x3x4o (full symmetry)
• x3x3x *b3x4x (half symmetry)