Great complex icosidodecahedron

Great complex icosidodecahedron
Type	Uniform star polyhedron
Elements	F = 32, E = 60 (30x2) V = 12 (χ = -16)
Faces by sides	20{3}+12{5/2}
Wythoff symbol	5 | 3 5/3
Symmetry group	Ih, [5,3], *532
Index references	U-, C-, W-
Dual polyhedron	Great complex icosidodecacron
Vertex figure	(3.5/3)5 (3.5/2)5/3
Bowers acronym	Gacid

In geometry, the great complex icosidodecahedron is a degenerate uniform star polyhedron. It has 12 vertices, and 60 (doubled) edges, and 32 faces, 12 pentagrams and 20 triangles. All edges are doubled (making it degenerate), sharing 4 faces, but are considered as two overlapping edges as topological polyhedron.

It can be constructed from a number of different vertex figures.

As a compound

The great complex icosidodecahedron can be considered a compound of the small stellated dodecahedron, {5/2,5}, and great icosahedron, {3,5/2}, sharing the same vertices and edges, while the second is hidden, being completely contained inside the first.

Compound polyhedron Small stellated dodecahedron Great icosahedron Compound See also Small complex icosidodecahedron Small complex rhombicosidodecahedron Complex rhombidodecadodecahedron Great complex rhombicosidodecahedron References Coxeter, Harold Scott MacDonald; Longuet-Higgins, M. S.; Miller, J. C. P. (1954), "Uniform polyhedra", Philosophical Transactions of the Royal Society of London. Series A. Mathematical and Physical Sciences 246 (916): 401–450, doi:10.1098/rsta.1954.0003, ISSN 0080-4614  (Table 6, degenerate cases) Weisstein, Eric W.. "Great complex icosidodecahedron". http://mathworld.wolfram.com/GreatComplexIcosidodecahedron.html.  Klitzing, Richard. "3D uniform polyhedra o5/3x3o5*a and o3/2x5/2o5*a - gacid". https://bendwavy.org/klitzing/dimensions/polyhedra-neu.htm.