These three paper sculptures together form a trio that highlight the three types of rotational symmetry in the icosahedral symmetry group. In the first, the parts have 2-fold rotational symmetry; in the second, the parts have 5-fold symmetry; and in the third, the parts have 3-fold symmetry. In each case, the design is composed of flat parts which lie in a plane orthogonal to the corresponding symmetry axes.
Each of the three orbs is designed with identical components (30, 12, and 20 parts, respectively) that interlock securely with small slits. No glue, tape, or other material is needed to hold them together.