Inverted prismatoicositetrachoron

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

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.

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).