In geometry, the small snub icosicosidodecahedron or snub disicosidodecahedron is a uniform star polyhedron, indexed as U32. It has 112 faces (100 triangles and 12 pentagrams), 180 edges, and 60 vertices. Its stellation core is a truncated pentakis dodecahedron. It also called a holosnub icosahedron, ß{3,5}. The 40 non-snub triangular faces form 20 coplanar pairs, forming star hexagons that are not quite regular. Unlike most snub polyhedra, it has reflection symmetries.

Convex hull

Its convex hull is a nonuniform truncated icosahedron.

Cartesian coordinates

Let be largest (least negative) zero of the polynomial, where \phi is the golden ratio. Let the point p be given by Let the matrix M be given by M is the rotation around the axis by an angle of 2\pi/5, counterclockwise. Let the linear transformations be the transformations which send a point (x, y, z) to the even permutations of with an even number of minus signs. The transformations T_i constitute the group of rotational symmetries of a regular tetrahedron. The transformations T_i M^j, constitute the group of rotational symmetries of a regular icosahedron. Then the 60 points T_i M^j p are the vertices of a small snub icosicosidodecahedron. The edge length equals -2\xi, the circumradius equals, and the midradius equals \sqrt{-\xi}. For a small snub icosicosidodecahedron whose edge length is 1, the circumradius is Its midradius is The other zero of P plays a similar role in the description of the small retrosnub icosicosidodecahedron.