Anne Tyng: Inhabiting Geometry The Graham Foundation 4 West Burton Place, Chicago Through June 18 ...

Platonic solids generate their four-dimensional analogues. Acta Crystallographica Section A Foundations of Crystallography, 2013; 69 (6): 592 DOI: 10.1107/S0108767313021442; ...

A69, 592-602; doi: 10.1107/S0108767313021442] shows how regular convex 4-polytopes, the analogues of the Platonic solids in four dimensions, ...

Salvatore Torquato and Yang Jiao now report the densest known packings of the 5 Platonic solids (tetrahedron, cube, octahedron, dodecahedron and icosahedron) and 13 Archimedean polyhedra.

Platonic solids, the first class of such shapes, are well-known. They consist of five different shapes: tetrahedron, cube, octahedron, dodecahedron, and icosahedron.