Regular polyhedron puzzles

In a geometrical puzzle having an external regular polyhedron structure with at least eight plane faces and having a core internal regular polyhedron structure, the external and internal structures being in the form of similar concentric regular polyhedrons with parallel faces and with each vertex of said internal regular polyhedron structure lying on the straight line which joins the corresponding vertex of said external regular polyhedron structure to the geometric center of the puzzle;

• said puzzle also having a hollow section inside said external regular polyhedron structure;
• said external regular polyhedron structure being further subdivided into component pieces along planes of rotation, one plane of rotation passing through each vertex of said core internal regular polyhedron structure and being orthogonal (perpendicular) to the straight line which passes through that vertex and through the center of the puzzle;
• the relative sizes of said concentric regular polyhedrons being such that each plane of rotation passing through a vertex of said core internal regular polyhedron structure passes through the geometric centers of all external faces of the puzzle which share in common the corresponding vertex of said external regular polyhedron structure;
• said component pieces are either (i) corner component pieces, one corner component piece corresponding to each vertex of said external regular polyhedron structure, or (ii) external edge component pieces, one external edge component piece corresponding to each edge of said external regular polyhedron structure;
• each corner component piece of said external regular polyhedron structure sits directly above and is joined to a vertex of said core internal polyhedron structure by means of a screw (pivot) having a smooth top part supported at its head and surrounded by a spring totally inside the corner component piece, the screw extends through the vertex of and is fixed to said core internal polyhedron structure;
• the screw is aligned such as to allow its associated corner component piece to rotate freely in place around the straight line which passes through that vertex and through the center of the puzzle;
• each external edge component piece has the general shape of a tetrahedron with two exposed triangular faces and with a knob adjoined to its unexposed edge;
• said knob fits in a groove to prevent disassembly;
• parts of the edges of each corner component piece which lie along a plane of rotation are cut off to form parts of grooves to accommodate the knobs of edge component pieces;
• each corner component piece and its adjacent edge component pieces are allowed to rotate together as a group above a plane of rotation around the straight line passing through the center of said puzzle and orthogonal to said plane of rotation;
• rotations of component structures alter the relative positions and the initial external surface designs;
• the object and challenge of the puzzle is to perform additional rotations to move the component structures back to their initial positions and to other interesting positions.

In a geometrical puzzle having an external regular polyhedron structure with at least eight plane faces and having a core internal spherical structure;

• said puzzle also having a hollow section inside said external regular polyhedron structure;
• said external regular polyhedron structure being further subdivided into corner and edge component pieces along planes of rotation, one plane of rotation associated with each vertex of said external regular polyhedron structure;
• said one plane of rotation passing through the point of intersection of the straight line joining its associated vertex to the center of the puzzle and of the surface of said core internal spherical structure, said one plane also being perpendicular to said straight line;
• the size of said core internal spherical structure being such that each plane of rotation associated with a vertex of said external regular polyhedron structure passes through the geometric centers of all the external faces of the puzzle which share that vertex in common;
• each corner component piece of said external regular polyhedron sits directly above a plane of rotation and is joined to the core internal spherical structure by means of a screw pivot having a smooth top part, said screw pivot is supported at its head and surrounded by a spring inside the corner component piece, the screw extends through and is fixed to said core internal spherical structure at the point where said plane of rotation meets said core internal spherical structure;
• each screw pivot is aligned such that each corner component piece is allowed to rotate freely in place around a straight line which passes through a vertex and the center of the puzzle;
• each edge external component piece has the general shape of a tetrahedron with two exposed triangular faces and with a knob adjoined to its unexposed edge;
• said knob fits in a groove to prevent disassembly;
• parts of the edges of each corner component piece which lie along a plane of rotation are cut off to form parts of grooves to accommodate the knobs of edge component pieces;
• each corner component piece and its adjacent edge component pieces are allowed to rotate together as a group above a plane of rotation around the straight line passing through the center of said puzzle and orhtogonal to said plane of rotation;
• rotations of component structures alter the relative positions and the initial external surface designs;
• the object and challenge of the puzzle is to perform additional rotations to move the component structures back to their initial positions and to other interesting positions.