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.

be the real zero of the polynomial

is known as the plastic ratio.

is the rotation around the axis

be the transformations which send a point

with an even number of minus signs.

constitute the group of rotational symmetries of a regular tetrahedron.

constitute the group of rotational symmetries of a regular icosahedron.

are the vertices of a snub icosidodecadodecahedron.

The edge length equals

+ ρ − 3 ϕ − 1

+ ρ − ϕ

For a snub icosidodecadodecahedron whose edge length is 1, the circumradius is Its midradius is The medial hexagonal hexecontahedron is a nonconvex isohedral polyhedron.

It is the dual of the uniform snub icosidodecadodecahedron.

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