Great retrosnub icosidodecahedron

In geometry, the great retrosnub icosidodecahedron or great inverted retrosnub icosidodecahedron is a nonconvex uniform polyhedron, indexed as U74.

It has 92 faces (80 triangles and 12 pentagrams), 150 edges, and 60 vertices.

[1] It is given a Schläfli symbol sr{3⁄2,5⁄3}.

be the smallest (most negative) zero of the polynomial

is the golden ratio.

is the rotation around the axis

Let the linear transformations

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 great snub icosahedron.

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 four positive real roots of the sextic in R2,

are the circumradii of the snub dodecahedron (U29), great snub icosidodecahedron (U57), great inverted snub icosidodecahedron (U69), and great retrosnub icosidodecahedron (U74).

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