(Redirected from Shafipto)
Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymShafipto
Coxeter diagram
Elements
Cells32 triangular prisms, 8 cubes, 8 small rhombicuboctahedra
Faces64 triangles, 48+96 squares
Edges96+96
Vertices64
Vertex figureIrregular triangular hemiantipodium, edge lengths 2 (top triangle and sides) and 1 (base pseudo-triangle)
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{3+\sqrt2}{2}} \approx 1.48563}$
Dichoral anglesSirco–4–cube: 90°
Sirco–3–trip: 90°
Sirco–4–trip: ${\displaystyle \arccos\left(\frac{\sqrt3}{3}\right) ≈ 54.73561°}$
Number of external pieces248
Level of complexity23
Related polytopes
ArmySidpith
RegimentSidpith
Abstract & topological properties
Euler characteristic32
OrientableNo
Properties
SymmetryB4, order 384
ConvexNo
NatureTame

The small hexadecafaceted prismatotesseractioctachoron, or shafipto, is a nonconvex uniform polychoron that consists of 8 cubes, 32 triangular prisms, and 8 small rhombicuboctahedra. One cube, three triangular prisms, and three small rhombicuboctahedra join at each vertex.

It also has 16 tetrahedra and 24 cubes as pseudofacets.

It can be constructed as a blend of four small rhombicuboctahedral prisms. In the process some of the cubical cells blend out. Alternatively, it can be thought of as a blend of four small cubicuboctahedral prisms. In the process the octagonal prism side cells blend with the base small cubicuboctahedra to produce the small rhombicuboctahedra.

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small disprismatotesseractihexadecachoron.