Snub dodecadodecahedron

In geometry, the snub dodecadodecahedron is a nonconvex uniform polyhedron, indexed as $U 40$ . It has 84 faces (60 triangles, 12 pentagons, and 12 pentagrams), 150 edges, and 60 vertices. It is given a Schläfli symbol $sr{.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}5⁄2,5},$ as a snub great dodecahedron.

Snub dodecadodecahedron

Type	Uniform star polyhedron
Elements	F = 84, E = 150 V = 60 (χ = −6)
Faces by sides	60{3}+12{5}+12{5/2}
Coxeter diagram
Wythoff symbol	\| 2 5/2 5
Symmetry group	I, [5,3]⁺, 532
Index references	U₄₀, C₄₉, W₁₁₁
Dual polyhedron	Medial pentagonal hexecontahedron
Vertex figure	3.3.5/2.3.5
Bowers acronym	Siddid

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