“It works because the floating tetrahedra want to fall apart into five pieces and the floating pentagons want to fall apart into six pieces,” Hart says. “They can’t agree on how to fall apart, so they end up staying together.”
Each of the two smaller structures has 30 sides: six pentagons with five sides each, and five tetrahedra with six edges each. Each pentagon side connects with a single tetrahedron edge — this is what gives the sculpture its solidity. Hart chose sharply waved edges for the pentagons and allowed the edges of his tetrahedra to stray from straight lines, undulating first up and then down in a wave. The sculpture is thus created from 30 laser-cut wood pieces, each containing one pentagon edge and one tetrahedron edge.
Hart built his sculpture on the underlying geometry of the rhombic triacontahedron, which is most familiar — if it’s familiar at all — as the 30-sided die in Dungeons & Dragons. (“Triacontahedron” is a mouthful, but it just means “30-sided solid figure with straight edges and flat faces.” “Rhombic” means that its faces are all rhombuses — parallelograms with sides of equal lengths.)
“I think of myself as an applied mathematician, applying math to sculpture,” Hart says. “Working three-dimensionally gives you a tactile understanding, a different way of knowing what’s happening. Like in any other branch of mathematics, you notice things that seem to work out, and you make conjectures, and that leads you to prove them or disprove them. It leads to mathematical questions.”
[This article originally appeared in print as "Visions of Math"]