Small retrospinoprismatodisicositetrachoron

The small retrospinoprismatodisicositetrachoron, or sarnipadi, is a nonconvex uniform polychoron that consists of 24 truncated cubes, 24 small rhombihexahedra, and 96 triangular prisms. Four truncated cubes, four small rhombihexahedra, and four triangular prisms join at each vertex.

Small retrospinoprismatodisicositetrachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sarnipadi
Elements
Cells	96 triangular prisms, 24 truncated cubes, 24 small rhombihexahedra
Faces	192 triangles, 288 squares, 144 octagons
Edges	576
Vertices	144
Measures (edge length 1)
Circumradius	${\sqrt {2+{\sqrt {2}}}}\approx 1.84776$
Dichoral angles	Tic–3–trip: 90°
	Sroh–8–tic: 45°
	Sroh–4–trip: $\arccos \left({\frac {\sqrt {6}}{3}}\right)\approx 35.26439^{\circ }$
Number of external pieces	5832
Level of complexity	187
Related polytopes
Army	Spic
Regiment	Spic
Conjugate	Great retrospinoprismatodisicositetrachoron
Abstract & topological properties
Flag count	11520
Euler characteristic	48
Orientable	No
Properties
Symmetry	F4, order 1152
Convex	No
Nature	Feral

It can be constructed as a blend of three small pseudorhombic prismatotesseracts. In the process the octagonal prisms blend into small rhombihexahedra.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 13: Spic and Giddic Regiments" (#526).