Great prismated 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

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.

Vertex coordinates

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

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

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)

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