Small retrofrustary prismatodisicositetrachoron

Small retrofrustary prismatodisicositetrachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sirfipdi
Elements
Cells	96 hexagonal prisms, 24 small rhombicuboctahedra, 24 quasirhombicuboctahedra
Faces	192 triangles, 144+288+288 squares, 96 hexagons
Edges	576+576
Vertices	288
Measures (edge length 1)
Circumradius	${\sqrt {2}}\approx 1.41421$
Hypervolume	70
Dichoral angles	Querco–4–hip: $\arccos \left(-{\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }$
	Hip–6–hip: 120°
	Querco–4–sirco: 90°
	Querco–3–sirco: 60°
	Sirco–4–hip: $\arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 54.73561^{\circ }$
Central density	-2
Related polytopes
Army	Cont, edge length ${\sqrt {2}}-1$
Regiment	Afdec
Conjugate	None
Abstract & topological properties
Flag count	16128
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	F4, order 1152
Convex	No
Nature	Tame

The small retrofrustary prismatodisicositetrachoron, or sirfipdi, is a nonconvex uniform polychoron that consists of 24 quasirhombicuboctahedra, 24 small rhombicuboctahedra, and 96 hexagonal prisms. Two quasirhombicuboctahedra, two small rhombicuboctahedra, and four hexagonal prisms join at each vertex.

It has the same cell counts as the great retrofrustary prismatodisicositetrachoron, but the quasirhombicuboctahedra and small rhombicuboctahedra are in different positions.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 15: Afdec Regiment" (#629).