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.

Photo Credit: fdecomite. 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 ...

The new shapes don’t fit into any of these categories. “This is the first new class of convex, equilateral polyhedra with icosahedral symmetry in 400 years,” says UCLA neuroscientist Stan ...

These polyhedra are sometimes called the Johnson solids. In 1969 the Russian Viktor A. Zalgaller offered a computer-based computational proof that Johnson had completed the enumeration of convex ...

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 ...

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 ...

However, for some polyhedra fewer measurements suffice; in the case of the cube we show that nine carefully chosen measurements are enough. We also prove a number of analogous results for planar ...

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 ...