Abstract: An oblique twistable 3-dimensional puzzle consists of an assemblage of parts where the organization of these parts is based on a guiding polyhedron which is an imagined oblique polyhedron. The guiding polyhedron is subdivided into pieces, with one center piece, and one piece for each face, edge, and vertex of said guiding polyhedron. The parts of said assemblage can be arranged so that for each part of said assemblage there is a corresponding piece of said subdivided guiding polyhedron and vice versa, and when said parts are so arranged they give the appearance of a single subdivided solid figure. The parts of said assemblage are held to one another by means pivotally connecting the face parts to the center part, and extensions of the edge and vertex parts with matching channels in the center, face, and edge parts. The parts corresponding to a face of said guiding polyhedron may be rotated as a block with respect to the other parts by 360.degree..