Abstract: One piece, injection-moldable, functionally polyhedral construction modules. The construction modules are thin-walled, cored out versions of a polyhedron. Each construction module comprises one polyhedron wall portion that is interiorly tangent to each face of at least one set of identical faces of a superimposed polyhedron template. Each polyhedron wall portion forms a complex with its tangent face of its superimposed polyhedron template that is the mirror image of at least half of such complexes. Each polyhedron wall portion is visible in both directions along a predetermined axis. Each polyhedron wall portion comprises an asymmetric aligning means that may include one or more snap-fit connectors. Every polyhedron wall portion is part of a single piece of material. Accordingly, these construction modules may be injection molded as single pieces of material, and, when they are aligned face-to-face, they exhibit the constructive properties of their polyhedron templates.

Abstract: A cube comprising a first set (18) of three identical, contiguous faces and a second set (19) of three identical, contiguous faces. The first set (18) has third order rotational symmetry about a common corner (20) and comprises a first face (22). The first face (22) comprises a male connector fin (36A), a female connector slot (38A), a first band (28A), and a second band (30A). The male connector fin (36A) and female connector slot (38A) lie parallel to, adjacent to, and on opposite sides of a diagonal (34) emanating from the common corner (20). The first band (28A) parallels the diagonal (34) and connects the midpoints of two edges of the first face (22). The second band (30A) mirrors the first band across the diagonal (34). The first set (18) and the second set (19) are enantiomers. Accordingly, a plurality of these cubes can be snapped together, face-to-face, to manifest a variety of tessellating band patterns.

Abstract: A system of releasable connectors moldable at various angles, comprising a male arch and a female slot. The male arch resembles an inverted V, having a substantially isosceles outline and a central void adjacent to its base. The female slot has two opposing and medially-facing projections midway along the long edges of its mouth. A secure but releasable connection is made when the male arch is inserted into the female slot, causing the projections of the female slot to become seated in the void of the male arch. Both the male arch and the female slot can be molded at a variety of angles. This feature allows them to be incorporated into multiple, differently-inclined regions of the same piece of molded material.