After 400 years, mathematicians find a new class of shapes

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The works of the Greek polymath Plato have kept people busy for millennia. Mathematicians have pondered Platonic solids, a collection of geometric forms that are highly regular and are frequently found in nature.

Platonic solids are generically termed equilateral convex polyhedra. In the millennia since Plato's time, only two other collections of equilateral convex polyhedra have been found: Archimedean solids (including the truncated icosahedron) and Kepler solids (including rhombic polyhedra). Nearly 400 years after the last class was described, mathematicians claim that they may have now identified a new, fourth class, which they call Goldberg polyhedra. In the process of making this discovery, they think that they’ve demonstrated that an infinite number of these solids could exist.

Platonic love for geometry

Equilateral convex polyhedra share a set of characteristics. First, each of the sides of the polyhedra needs to be the same length. Second, the shape must be completely solid—that is, it must have a well-defined inside and outside that is separated by the shape itself. Third, any point on a line that connects two points in the shape must never fall outside of it