Great prismated tesseractic tetracomb

Great prismated tesseractic tetracomb
Rank	5
Type	Uniform
Space	Euclidean
Notation
Bowers style acronym	Gippittit
Coxeter diagram	x4x3x3x4o ()
Elements
Tera	6N square-octagonal duoprisms, 4N truncated octahedral prisms, N truncated icositetrachora, N great disprismatotesseractihexadecachora
Cells	24N+24N cubes, 32N hexagonal prisms, 24N octagonal prisms, 8N+16N truncated octahedra, 4N great rhombicuboctahedra
Faces	48N+48N+96N+96N squares, 32N+64N hexagons, 24N octagons
Edges	96N+96N+96N+192N
Vertices	192N
Vertex figure	Sphenoidal pyramid, edge lengths √2 (6), √3 (3), √2+√2 (1)
Related polytopes
Army	Gippittit
Regiment	Gippittit
Conjugate	Great quasiprismated tesseractic tetracomb
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	R5
Convex	Yes
Nature	Tame

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:

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

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)

External links

• Klitzing, Richard. "gippittit".
• Wikipedia contributors. "Runcicantitruncated tesseractic honeycomb".