Quasirhombicosidodecahedron

The quasirhombicosidodecahedron, also commonly known as simply the nonconvex great rhombicosidodecahedron, or qrid is a uniform polyhedron. It consists of 20 triangles, 30 squares, and 12 pentagrams, with one triangle, two squares, and one pentagram meeting at each vertex. It can be obtained by quasicantellation of the great stellated dodecahedron or great icosahedron, or equivalently by pushing either polyhedron's faces inward and filling the gaps with appropriate faces.

It is also sometimes called a great rhombicosidodecahedron, but is not to be confused with the convex polyhedron with the same name.

It is a faceting of the great dodecicosidodecahedron, using the original's 12 pentagrams and 20 triangles along with 30 additional squares.

Vertex coordinates
Its vertices are the same as those of its regiment colonel, the great dodecicosidodecahedron.