Small dodecicosidodecahedron

Small dodecicosidodecahedron

Type	Uniform star polyhedron
Elements	F = 44, E = 120 V = 60 (χ = −16)
Faces by sides	20{3}+12{5}+12{10}
Wythoff symbol	³/₂ 5 \| 5 3 5/4 \| 5
Symmetry group	I_h, [5,3], *532
Index references	U₃₃, C₄₂, W₇₂
Dual polyhedron	Small dodecacronic hexecontahedron
Vertex figure	5.10.³/₂.10
Bowers acronym	Saddid

In geometry, the small dodecicosidodecahedron is a nonconvex uniform polyhedron, indexed as U₃₃. Its vertex figure is a crossed quadrilateral.

Related polyhedra

It shares its vertex arrangement with the small stellated truncated dodecahedron and the uniform compounds of 6 or 12 pentagrammic prisms. It additionally shares its edge arrangement with the rhombicosidodecahedron (having the triangular and pentagonal faces in common), and with the small rhombidodecahedron (having the decagonal faces in common).

Rhombicosidodecahedron	Small dodecicosidodecahedron	Small rhombidodecahedron
Small stellated truncated dodecahedron	Compound of six pentagrammic prisms	Compound of twelve pentagrammic prisms

Small dodecacronic hexecontahedron

Type	Star polyhedron
Face
Elements	F = 60, E = 120 V = 44 (χ = −16)
Symmetry group	I_h, [5,3], *532
Index references	DU₃₃
dual polyhedron	Small dodecicosidodecahedron

The dual polyhedron to the small dodecicosidodecahedron is the small dodecacronic hexecontahedron. It is visually identical to the small rhombidodecacron.

Coxeter, H. S. M. (May 13, 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.
Wenninger, Magnus (1974). Polyhedron Models. Cambridge University Press. ISBN 0-521-09859-9. OCLC 1738087.
Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 730208

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