Small complex rhombicosidodecahedron

Small complex rhombicosidodecahedron
Rank	3
Type	Uniform
Notation
Bowers style acronym	Sicdatrid
Coxeter diagram	x5/2o3x ()
Elements
Faces	20 triangles, 30 squares, 12 pentagrams
Edges	60+60
Vertices	20
Edge figure	Tetrad
Measures (edge length 1)
Circumradius	${\frac {\sqrt {3}}{2}}\approx 0.86603$
Central density	7
Related polytopes
Army	Doe, edge length ${\frac {{\sqrt {5}}-1}{2}}$
Regiment	Sidtid
Conjugate	Great complex rhombicosidodecahedron
Convex hull	Dodecahedron
Abstract & topological properties
Flag count	480
Euler characteristic	-38
Properties
Symmetry	H3, order 120
Convex	No

The small complex rhombicosidodecahedron, or sicdatrid, is a degenerate uniform exotic polyhedroid. It consists of 12 pentagrams, 20 triangles, and 30 squares. 3 pentagrams, 3 triangles, and 6 squares join at each vertex. It can be constructed as a cantellated great icosahedron or great stellated dodecahedron. It can also be seen as a compound of a small ditrigonary icosidodecahedron and a rhombihedron, the compound of 5 cubes, with their edges merging into tetradic edges.

External links

• Klitzing, Richard. "sicdatrid".