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.
Evidence: It has 18 faces (12 pentagrams and 6 decagrams), 60 edges, and 30 vertices. 
Elements F = 18, E = 60
V = 30 (χ = −12)