Snub dodecadodecahedron

In geometry, the snub dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U40.

It has 84 faces (60 triangles, 12 pentagons, and 12 pentagrams), 150 edges, and 60 vertices.

[1] It is given a Schläfli symbol sr{5⁄2,5}, as a snub great dodecahedron.

be the smallest real zero of the polynomial

the golden ratio.

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 dodecadodecahedron.

The edge length equals

, the circumradius equals

, and the midradius equals

For a great snub icosidodecahedron whose edge length is 1, the circumradius is Its midradius is The other real root of P plays a similar role in the description of the Inverted snub dodecadodecahedron The medial pentagonal hexecontahedron is a nonconvex isohedral polyhedron.

It is the dual of the snub dodecadodecahedron.

It has 60 intersecting irregular pentagonal faces.

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