Small spinoprismatotesseractioctachoron

The small spinoprismatotesseractioctachoron, or snipto, is a nonconvex uniform polychoron that consists of 8+24 cubes and 8 small rhombihexahedra. Four cubes and three small rhombihexahedra join at each vertex.

Small spinoprismatotesseractioctachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Snipto
Elements
Cells	8+24 cubes, 8 small rhombihexahedra
Faces	48+96 squares, 24 octagons
Edges	96+96
Vertices	64
Vertex figure	Triangular crown, edge lengths √2 (top triangles and side edges of triangles) and √2+√2 (edges between butterflies)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{3+\sqrt2}{2}} \approx 1.48563$
Dichoral angles	Cube–4–cube: 135°
	Sroh–8–sroh: 90°
	Sroh–4–cube: 90°
Number of external pieces	128
Level of complexity	13 13
Related polytopes
Army	Sidpith
Regiment	Sidpith
Conjugate	Great spinoprismatotesseractioctachoron
Abstract & topological properties
Euler characteristic	0
Orientable	No
Properties
Symmetry	B4, order 384
Convex	No
Nature	Wild

It can be constructed as a blend of six square-octagonal duoprisms. In the process some of the cubes blend out, while the octagonal prisms blend into small rhombihexahedra.

Gallery

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 11: Antipodiumverts" (#453).