Curvilinear polyhedral construction kit

A construction kit for forming an entirely curvilinearly faced polyhedron, all surfaces of which are curved surfaces laterally defined exclusively by arcs, from a planar polygonal component defined exclusively by arcuate edges and being scored exclusively along arcuate interior lines to form arcuately defined polygons to facilitate the folding and assembly of said component to form said polyhedron.

A planar multilobate disc element of a kit for constructing curvilinear faced polyhedrons from stiff scorable sheet material, the outer edges of said element being from three to six identical symmetrical convex exterior arcs connected end-to-end in a closed chain, each of said exterior arcs being opposed by an identical scored concave interior arc, said interior arcs intersecting each other only at the aforesaid connected ends of said exterior arcs, whereby said scored interior arcs together with their respective opposed exterior arcuate edges of said element define a closed peripheral chain of from three to six congruent symmetrical two-pointed interiorly unscored lobes surrounding an interiorly unscored equilateral polygonal face, said element being readily foldable only along said scored interior arcs.

A planar multilobate disc element of a kit for constructing curvilinear faced polyhedrons from stiff scorable sheet material, the outer edges of said element being from three to five identical symmetrical convex exterior arcs connected end-to-end and in a closed chain, each of said exterior arcs being opposed by an identical scored concave interior arc, said interior arcs intersecting each other only at the aforesaid connected ends of said exterior arcs, whereby said scored interior arcs together with their respective opposed exterior arcuate edges of said element define a closed peripheral chain of from three to five congruent symmetrical two-pointed interiorly unscored lobes surrounding an interiorly unscored regular polygonal face, said element being readily foldable only along said scored interior arcs.

A planar component of a kit for constructing curvilinear faced polyhedrons from stiff scorable sheet material, the outer edges of said component being a plurality of identical symmetrical convex exterior arcs connected end-to-end in a closed chain, each of said exterior arcs being opposed by an identical scored concave interior arc, said interior arcs intersecting each other only at the aforesaid connected ends of said exterior arcs, whereby the aforesaid scored interior arcs together with their respective opposed exterior arcuate edges of said component define a closed peripheral chain of congruent symmetrical two-pointed interiorly unscored lobes connected end-to-end, at least one of said end connections of said exterior lobes being further connected to at least one non-adjacent end connection of said exterior lobes by at least one bilaterally arcuately scored interior lobe which is also interiorly unscored and congruent to said exterior lobes, whereby said connected congruent exterior and interior lobes collectively define a plurality of interiorly unscored equilateral polygonal faces, each said polygonal face having from three to six sides, said component being readily foldable only along said scored interior arcs.

A closed curvilinear faced polyhedron formed from stiff scorable planar material, said material having been scored and folded exclusively along a plurality of identical symmetrical arcs to define a plurality of faces of said polyhedron, each said face being an interiorly unscored equilateral polygon having from three to six curvilinear side edges curved concavely relative to the center of said polygonal face, each said face being curved convexly relative to the center of said polyhedron and being in point-to-point contact with at least one other face of said polyhedron, each side edge of each said face being separated from a side edge of an adjacent face by an interiorly unscored symmetrical two-pointed lobe having convexly curved side edges, all of said lobes of said polyhedron being congruent and curved concavely relative to the center of said polyhedron.