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The idea for the new map projection came from a recent paper I wrote, “Envelope Polyhedra,” introducing new class of regular polyhedra in which polygons are allowed to appear back-to-back.

His office overflowed with books, journals, food wrappers and paper polyhedrons, many dangling from the ceiling.

He notes that his team took inspiration from the Greek philosopher Plato, who related each of the four classical elements—earth, air, fire, and water—to a regular polyhedron, coincidentally linking earth with the cube.

This year’s exhibit also features updated versions of the popular “Celestial Shadows” display of spinning polyhedrons, the “Lightwave Lake” light show and Jen Lewin’s interactive landscape of meandering pathways called “Aqueous.”

This highly symmetric, cage-like shape was first described by Archimedes, and the rules that guide the topology of polyhedra were first developed by Descartes.