Platonic love for geometry Equilateral convex polyhedra need to have certain characteristics. First, each of the sides of the polyhedra needs to be of the same length. Second, the shape must be ...

Since Plato’s work, two other classes of equilateral convex polyhedra, as the collective of these shapes are called, have been found: Archimedean solids (including truncated icosahedron) and ...

Scientists discover a new SHAPE for the first time in 400 years (but it just looks like a football) U.S. mathematicians believe they have identified a fourth class of ‘equilateral convex ...

The shapes’ flat faces make them convex polyhedra, a type of highly symmetric, faceted solid first studied by the ancient Greeks.

Any two points on a convex polyhedron many be joined by a line that is entirely inside the polyhedron. One of the most familiar uniform convex polyhedron is the cube, which has six square faces that ...

Mathematics of Operations Research, Vol. 5, No. 4 (Nov., 1980), pp. 576-594 (19 pages) We introduce the property of k-decomposability for simplicial complexes which, if satisfied by the dual ...

If nothing else, Schein's work may prod mathematicians to find other interesting geometric shapes, now that equilateral convex polyhedra have a new family. PNAS, 2014.

Goldberg polyhedron. During this work, Schein came across the work of 20th century mathematician Michael Goldberg who described a set of new shapes, which have been named after him, as Goldberg ...