Claim: Great dodecahemidodecacron, a star polyhedron with 30 faces, 60 edges and 18 vertices is the dual of  the great dodecahemidodecahedron, a nonconvex uniform polyhedron that has 18 faces (12 pentagrams and 6 decagrams), 60 edges, and 30 vertices.
Evidence: Star polyhedron F = 30, E = 60
V = 18 (χ = −12) In geometry, the great dodecahemidodecacron is the dual of the great dodecahemidodecahedron, and is one of nine dual hemipolyhedra. In geometry, the great dodecahemidodecahedron is a nonconvex uniform polyhedron, indexed as U70. It has 18 faces (12 pentagrams and 6 decagrams), 60 edges, and 30 vertices.