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. It is given a Schläfli symbol sr{ 3/2,5/3}.

Cartesian coordinates

Let be the smallest (most 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 great snub icosahedron. The edge length equals, the circumradius equals , and the midradius equals -\xi. 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).