Snub icosidodecadodecahedron

Snub icosidodecadodecahedron
Type	Uniform star polyhedron
Elements	F = 104, E = 180 V = 60 (χ = −16)
Faces by sides	(20+60){3}+12{5}+12{5/2}
Wythoff symbol	| 5/3 3 5
Symmetry group	I, [5,3]+, 532
Index references	U46, C58, W112
Dual polyhedron	Medial hexagonal hexecontahedron
Vertex figure	3.3.3.5.3.5/3
	Sided

3D model of a snub icosidodecadodecahedron

In geometry, the snub icosidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U₄₆. It has 104 faces (80 triangles, 12 pentagons, and 12 pentagrams), 180 edges, and 60 vertices.^[1] As the name indicates, it belongs to the family of snub polyhedra.

The circumradius of the snub icosidodecadodecahedron with unit edge length is

${\displaystyle {\frac {1}{2}}{\sqrt {\frac {2\rho -1}{\rho -1}}},}$

where ρ is the plastic constant, or the unique real root of ρ³ = ρ + 1.^[2]

Related polyhedra[]

Medial hexagonal hexecontahedron[]

Medial hexagonal hexecontahedron
Type	Star polyhedron
Face
Elements	F = 60, E = 180 V = 104 (χ = −16)
Symmetry group	I, [5,3]+, 532
Index references	DU46
dual polyhedron	Snub icosidodecadodecahedron

3D model of a medial hexagonal hexecontahedron

The medial hexagonal hexecontahedron is a nonconvex isohedral polyhedron. It is the dual of the uniform snub icosidodecadodecahedron.

See also[]

• List of uniform polyhedra

References[]

• Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208

External links[]

• Weisstein, Eric W. "Medial hexagonal hexecontahedron". MathWorld.

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