Snub icosidodecadodecahedron
In geometry, the snub icosidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U46. It has 104 faces, 180 edges, and 60 vertices. As the name indicates, it belongs to the family of snub polyhedra.
Cartesian coordinates
Let be the real zero of the polynomial. The number is known as the plastic ratio. Denote by the golden ratio. Let the point be given byLet the matrix be given by
is the rotation around the axis by an angle of, counterclockwise. Let the linear transformations
be the transformations which send a point to the even permutations of with an even number of minus signs.
The transformations constitute the group of rotational symmetries of a regular tetrahedron.
The transformations , constitute the group of rotational symmetries of a regular icosahedron.
Then the 60 points are the vertices of a snub icosidodecadodecahedron. The edge length equals, the circumradius equals, and the midradius equals.
For a snub icosidodecadodecahedron whose edge length is 1,
the circumradius is
Its midradius is