Prismatotetracontoctintercepted icositetrachoron

Prismatotetracontoctintercepted icositetrachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Picni
Elements
Cells	96 triangular prisms, 24+24 truncated cubes, 24 small rhombicuboctahedra
Faces	192+192 triangles, 72+288 squares, 144 octagons
Edges	288+288
Vertices	144
Measures (edge length 1)
Circumradius	${\sqrt {2+{\sqrt {2}}}}\approx 1.84776$
Dichoral angles	Sirco–4–sirco: 90°
	Tic–3–trip: 90°
	Sirco–3–tic: 60°
	Tic–8–tic: 45°
	Sirco–4–trip: $\arccos \left({\frac {\sqrt {6}}{3}}\right)\approx 35.26439^{\circ }$
Number of external pieces	1848
Level of complexity	51
Related polytopes
Army	Spic
Regiment	Spic
Conjugate	Prismatoicositetritetracontoctachoron
Abstract & topological properties
Flag count	14976
Euler characteristic	288
Orientable	No
Properties
Symmetry	F4, order 1152
Convex	No
Nature	Wild

The prismatotetracontoctintercepted icositetrachoron, or picni, is a nonconvex uniform polychoron that consists of 48 truncated cubes, 24 small rhombicuboctahedra, and 96 triangular prisms. Eight truncated cubes, four small rhombicuboctahedra and four triangular prisms join at each vertex.

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" (#522).