Icositetrintercepted prismatotetracontoctachoron

Icositetrintercepted prismatotetracontoctachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Inpac
Elements
Cells	24+24 octahedra 96 triangular prisms 24 small rhombicuboctahedra
Faces	192+192 triangles 72+288 squares
Edges	288+288
Vertices	144
Measures (edge length 1)
Circumradius	${\sqrt {2+{\sqrt {2}}}}\approx 1.84776$
Hypervolume	$43+30{\sqrt {2}}\approx 85.42641$
Dichoral angles	Oct–3–trip: 150°
	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	624
Level of complexity	23
Related polytopes
Army	Spic
Regiment	Spic
Conjugate	Icositetraretrointercepted prismatotetracontoctachoron
Abstract & topological properties
Flag count	10368
Euler characteristic	144
Orientable	Yes
Properties
Symmetry	F4, order 1152
Flag orbits	9
Convex	No
Nature	Wild

The icositetrintercepted prismatotetracontoctachoron, or inpac, is a nonconvex uniform polychoron that consists of 24+24 octahedra, 24 small rhombicuboctahedra and 96 triangular prisms. Two octahedra, 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" (#521).

• Klitzing, Richard. "inpac".