Abstract: A multi-faceted solid geometrical puzzle toy includes a generally spherical base member and a plurality of tile members secured to the exterior of the base member, each tile member comprising one facet of the solid. In one embodiment, a plurality of regular pentagonal members are secured to the sphere in equally spaced apart relationship, the pentagonal members being raised from the surface of the sphere. The tile members include flanges extending laterally from inner portions thereof to be retained between the base member and the pentagonal members in translatable fashion. The gaps between adjacent pentagonal members define tracks in which the tile members may translate. The tile members include planar outer faces having linear edge portions disposed to impinge upon like linear edge portions of adjacent tile members to define a regular polyhedron, such as an icosahedron.