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icosidodecadodecahedron

n. a polyhedron having 44 faces, 60 vertices, 120 edges, 12 self intersected faces and 12 nonconvex faces

Wikipedia
Icosidodecadodecahedron

In geometry, the icosidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U. Its vertex figure is a crossed quadrilateral.