Small hexadecafaceted prismatotesseractioctachoron

Small hexadecafaceted prismatotesseractioctachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Shafipto
Coxeter diagram
Elements
Cells	32 triangular prisms, 8 cubes, 8 small rhombicuboctahedra
Faces	64 triangles, 48+96 squares
Edges	96+96
Vertices	64
Vertex figure	Irregular triangular hemiantipodium, edge lengths √2 (top triangle and sides) and 1 (base pseudo-triangle)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{3+\sqrt2}{2}} \approx 1.48563$
Dichoral angles	Sirco–4–cube: 90°
	Sirco–3–trip: 90°
	Sirco–4–trip: $\arccos\left(\frac{\sqrt3}{3}\right) ≈ 54.73561°$
Number of external pieces	248
Level of complexity	23
Related polytopes
Army	Sidpith
Regiment	Sidpith
Conjugate	Great hexadecafaceted prismatotesseractioctachoron
Abstract & topological properties
Euler characteristic	32
Orientable	No
Properties
Symmetry	B4, order 384
Convex	No
Nature	Tame

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.

Gallery

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 11: Antipodiumverts" (#449).

• Klitzing, Richard. "shafipto".