It's not necessarily perfect, but when you look at this three-dimensional shape pieced together with paper and tape, it feels oddly amusing. The way the shapes fit together in a seemingly seamless fashion makes this polygonal creation look almost unreal. And theoretically, it should be impossible to make something like this, let alone for it to exist in the realm of mathematics. But what seems impossible in theory can sometimes be made possible as the rules are bent in the practical, real world.
It is a new example of an unexpected class of mathematical objects that the American mathematician Norman Johnson stumbled upon in the 1960s. Johnson was working to complete a project started over 2,000 years earlier by Plato: to catalog geometric perfection. Among the infinite variety of three-dimensional shapes, just five can be constructed out of identical regular polygons: the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. If you mix and match polygons, you can form another 13 shapes from regular polygons that meet the same way at every vertex—the Archimedean solids—as well as prisms (two identical polygons connected by squares) and “anti-prisms” (two identical polygons connected by equilateral triangles).
(Image credit: Craig Kaplan/Nautilus)
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