# Great prismated cubic honeycomb

Great prismated cubic honeycomb
Rank4
Typeuniform
SpaceEuclidean
Notation
Bowers style acronymGippich
Coxeter diagramx4x3x4x ()
Elements
Cells3N octagonal prisms, N great rhombicuboctahedra
Faces6N+12N squares, 8N hexagons, 6N octagons
Edges24N+24N
Vertices24N
Vertex figurePhyllic disphenoid, edge lengths 2 (3), 3 (2), and 2+2 (1)
Measures (edge length 1)
Vertex density${\displaystyle 30\sqrt2-42 \approx 0.42640687119}$
Dual cell volume${\displaystyle \frac{7+5\sqrt2}6 \approx 2.34517796864}$
Related polytopes
ArmyGippich
RegimentGippitch
DualPhyllic disphenoidal honeycomb
ConjugateQuasiquasiprismated cubic honeycomb
Topological properties
OrientableYes
Properties
SymmetryR4×2
ConvexYes

The great prismated cubic honeycomb, or gippich, also known as the omnitruncated cubic honeycomb, or otch, is a convex uniform honeycomb. 2 great rhombicuboctahedra and 2 octagonal prisms join at each vertex of this honeycomb. As the name suggests, it is the omnitruncate of the R4 family.

This honeycomb can be alternated into a snub bicubic honeycomb, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create an edge-snub cubic honeycomb, cantic bisnub cubic honeycomb or great birhombitetrahedral honeycomb, which are nonuniform.

## Vertex coordinates

The vertices of a great prismated cubic honeycomb of edge length 1 are given by all permutations of:

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

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

## Related polytopes

o4o3o4o truncations
Name OBSA Schläfli symbol CD diagram Picture
Cubic honeycomb chon {4,3,4}
Truncated cubic honeycomb tich t{4,3,4}
Rectified cubic honeycomb rich r{4,3,4}
Bitruncated cubic honeycomb batch 2t{4,3,4}
Rectified cubic honeycomb rich r{4,3,4}
Truncated cubic honeycomb tich t{4,3,4}
Cubic honeycomb chon {4,3,4}
Small rhombated cubic honeycomb srich rr{4,3,4}
Great rhombated cubic honeycomb grich tr{4,3,4}
Small rhombated cubic honeycomb srich rr{4,3,4}
Great rhombated cubic honeycomb grich tr{4,3,4}
Small prismated cubic honeycomb = Cubic honeycomb chon t0,3{4,3,4}
Prismatorhombated cubic honeycomb prich t0,1,3{4,3,4}
Prismatorhombated cubic honeycomb prich t0,1,3{4,3,4}
Great prismated cubic honeycomb gippich t0,1,2,3{4,3,4}