Small rhombic disicositetrachoron

Small rhombic disicositetrachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sirdi
Elements
Cells	96 triangular prisms, 24 truncated cubes, 24 small rhombihexahedra
Faces	192 triangles, 288 squares, 144 octagons
Edges	288+576
Vertices	288
Vertex figure	Butterfly wedge, edge lengths 1 (bases), √2 (sides of outer triangles), and √2+√2 (sides of inner triangles)
Measures (edge length 1)
Circumradius	${\sqrt {4+2{\sqrt {2}}}}\approx 2.61313$
Dichoral angles	Sroh–4–trip: $\arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }$
	Sroh–8–tic: 45°
	Tic–3–trip: 30°
Related polytopes
Army	Srico
Regiment	Srico
Conjugate	Great rhombic disicositetrachoron
Convex core	Semi-uniform truncated icositetrachoron
Abstract & topological properties
Flag count	11520
Euler characteristic	–96
Orientable	No
Properties
Symmetry	F4, order 1152
Convex	No
Nature	Tame

The small rhombic disicositetrachoron, or sirdi, is a nonconvex uniform polychoron that consists of 24 truncated cubes, 24 small rhombihexahedra, and 96 triangular prisms. 2 of each type of cell join at each vertex.

It can be constructed as the blend of 3 prismatorhombated hexadecachora, with the cuboctahedron cells blending out and the octagonal prisms blending into small rhombihexahedra.

Vertex coordinates

The vertices are the same as those of the regiment colonel, the small rhombated icositetrachoron.

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#153).