(Redirected from Gahfipto)
Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymGahfipto
Coxeter diagram
Elements
Cells32 triangular prisms, 8 cubes, 8 quasirhombicuboctahedra
Faces64 triangles, 48+96 squares
Edges96+96
Vertices64
Vertex figureTriangular hemipodium, edge lengths 2 (top triangle and sides) and 1 (base pseudo-triangle)
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{3-\sqrt2}{2}} ≈ 0.89045}$
Dichoral anglesQuerco–4–cube: 90°
Querco–3–trip: 90°
Querco–4–trip: ${\displaystyle \arccos\left(\frac{\sqrt3}{3}\right) ≈ 54.73561°}$
Number of external pieces2824
Level of complexity343
Related polytopes
ArmyTat
RegimentGittith
Abstract & topological properties
Euler characteristic32
OrientableNo
Properties
SymmetryB4, order 384
ConvexNo
NatureTame

The great hexadecafaceted prismatotesseractioctachoron, or gahfipto, is a nonconvex uniform polychoron that consists of 8 quasirhombicuboctahedra, 8 cubes, and 32 triangular prisms. Three quasirhombicuboctahedra, one cube, and three triangular prisms join at each vertex.

It also has 16 tetrahedra and 24 cubes as pseudofacets.

It can be constructed as a blend of four quasirhombicuboctahedral prisms. In the process some of the cubical cells blend out. Alternatively, it can be thought of as a blend of four great cubicuboctahedral prisms. In the process the octagrammic prism side cells blend with the base great cubicuboctahedra to produce the quasirhombicuboctahedra.

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the great tesseractitesseractihexadecachoron.