Inverted prismatoicositetrachoron

The inverted prismatoicositetrachoron, or ipi, is a nonconvex uniform polychoron that consists of 24 small rhombicuboctahedra and 96 triangular prisms. Four small rhombicuboctahedra and four triangular prisms join at each vertex.

Inverted prismatoicositetrachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Ipi
Elements
Cells	96 triangular prisms, 24 small rhombicuboctahedra
Faces	192 triangles, 72+288 squares
Edges	288+288
Vertices	144
Vertex figure	Blend of two wedges, edge lengths 1 (blended wedge bases) and √2 (sides and top edges of wedges)
Measures (edge length 1)
Circumradius	${\sqrt {2+{\sqrt {2}}}}\approx 1.84776$
Dichoral angles	Sirco–4–sirco: 90°
	Sirco–4–trip: $\arccos \left({\frac {\sqrt {6}}{3}}\right)\approx 35.26439^{\circ }$
	Sirco–3–trip: 30°
Number of external pieces	600
Level of complexity	19
Related polytopes
Army	Spic
Regiment	Spic
Conjugate	Retroinverted prismatoicositetrachoron
Abstract & topological properties
Flag count	8064
Euler characteristic	0
Orientable	No
Properties
Symmetry	F4, order 1152
Flag orbits	7
Convex	No
Nature	Tame

It can be constructed as the blend of 3 small rhombated tesseracts, with the octahedral cells blending out.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 13: Spic and Giddic Regiments" (#520).