Prismatofaceted tetracontoctidisicositetrachoron

Prismatofaceted tetracontoctidisicositetrachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Pifficdi
Elements
Cells	96 triangular prisms, 24+24 octahedra, 24 truncated cubes, 24 small rhombihexahedra
Faces	192+192 triangles, 288 squares, 144 octagons
Edges	288+288
Vertices	144
Measures (edge length 1)
Circumradius	${\sqrt {2+{\sqrt {2}}}}\approx 1.84776$
Dichoral angles	Oct–3–trip: 150°
	Oct–3–tic: 60°
	Sroh–8–tic: 45°
	Sroh–4–trip: $\arccos \left({\frac {\sqrt {6}}{3}}\right)\approx 35.26439^{\circ }$
Number of external pieces	1200
Level of complexity	30
Related polytopes
Army	Spic
Regiment	Spic
Conjugate	Diretroprismatotetracontoctidisicositetrachoron
Abstract & topological properties
Flag count	13824
Euler characteristic	192
Orientable	No
Properties
Symmetry	F4, order 1152
Convex	No
Nature	Wild

The prismatofaceted tetracontoctidisicositetrachoron, or pifficdi, is a nonconvex uniform polychoron that consists of 48 octahedra, 24 truncated cubes, 24 small rhombihexahedra, and 96 triangular prisms. Two octahedra, four truncated cubes, four small rhombihexahedra, and four triangular prisms join at each vertex.

It has the same cell counts as the diretroprismatodisicositetritetracontoctachoron, but the small rhombihexahedra and triangular prisms are in different positions.

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" (#528).