A model of a dissected rhombic dodecahedron by A. Harry Wheeler, rearranged as two cubes. Smithsonian Institution negative numbers JN2012-0969 and JN2012-0966

During the 1930s, high school mathematics teacher A. Harry Wheeler (1873–1950) of Worcester, Massachusetts, built several models of polyhedra that could be divided and rearranged to form other polyhedra. The pieces of this colorful plastic model show either an orange-colored rhombic dodecahedron or, if rearranged, two cubes with faces like those of dice. Wheeler sometimes called this construction “Pair-a-Dice.” When the objects first came into the museum, the two parts had been separated and were subsequently assigned separate museum catalog numbers.

Images of a series of dissected polyhedra by Wheeler and at least one of his students are shown at: https://americanhistory.si.edu/collections/object-groups/geometric-models-dissected-polyhedra.