In the beginning, the alien artifact had been a black tetrahedron-the simplest and most fundamental of all regular solids, formed of four equal triangles.

Two thousand years later Dalton's atomic theory would show this idea to be along the right lines, though not related directly to the regular solids.

The book continues Euclid's comparison of regular solids inscribed in spheres.

Leonardo drew the illustrations of the regular solids while he lived with and took mathematics lessons from Pacioli.

To understand its appeal, consider the "regular solids": the sphere and the 5-member set of Platonic Solids.

All six regular solids share many symmetries.

The data were vital, but so was the preconception that the planetary orbits could be inscribed within, and circumscribed without, the five regular Greek solids.

They are completely regular solids: each has all of its faces repeating a regular polygon, triangle, square or pentagon.

Symmetry is the stuff of paradise: the home of Plato's perfect, regular solids.

Leonardo prepared a series of drawings of regular solids in a skeletal form to be engraved as plates.