Diretroprismatotetracontoctidisicositetrachoron

The diretroprismatotetracontoctidisicositetrachoron, or dirpicdi, is a nonconvex uniform polychoron that consists of 48 octahedra, 24 quasitruncated hexahedra, 24 great rhombihexahedra, and 96 triangular prisms. Two octahedra, four quasitruncated hexahedra, four great rhombihexahedra, and four triangular prisms join at each vertex.

Diretroprismatotetracontoctidisicositetrachoron
Rank	4
Type	Uniform
Notation
Bowers style acronym	Dirpicdi
Elements
Cells	48 oct, 24 quith, 24 groh, 96 trip
Faces	384 triangles, 288 squares, 144 octagrams
Edges	576
Vertices	144
Measures (edge length 1)
Circumradius	${\sqrt {2-{\sqrt {2}}}}\approx 0.76537$
Related polytopes
Army	Spic
Regiment	Giddic
Conjugate	Pifficdi
Abstract & topological properties
Euler characteristic	192
Orientable	No
Properties
Symmetry	F4, order 1152
Convex	No
Nature	Wild

It has the same cell counts as the icositetrifaceted prismatoicositetritetracontoctachoron, but the great rhombihexahedra and triangular prisms are in different positions.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the great distetracontoctachoron.

External links

• Bowers, Jonathan. "Category 13: Spic and Giddic Regiments" (#547).