Glass Geometry

The regular solids

Platonic Solids

The five Platonic Solids are the basis for all other solid geometry. And they have intrigued and inspired great philosophers, astronomers, mathematicians and so many more people from the ancient Greek days to, what is now called (I think), the New Age.

Plato (427 - 347 BC) described these shapes and developed a "nuclear" theory based on a prescribed relationship of the cube to earth, the tetrahedron to fire, the octahedron to air and the icosahedron to water. The dodecahedron was unique; it could not be combined with other "molecules" or broken down into different substances. Therefore it became the vessel that holds the world and the universe, the all uniting essential ingredient: the "Quinta Essentia."

Archimedes (287 - 212 BC) described thirteen more bodies that he found by truncation, that is cutting the points of a regular solid off in an equal fashion. One of the thirteen can be seen here in this life size paper mock-up of a lamp, describing the regular transition from a cube to an octahedron. It is the middle one, the cuboctahedron.

Johannes Kepler (1571 - 1630 AD), an astronomer, tried to relate the spheres of the Platonic Solids to the orbits of the planets. This proved to be impossible, since the orbits are ellyptical, not circular. He did discover two more regular solids: the stellations of the icosahedron and dodecahedron.

Later, but unawares of the work of Kepler, Louis Poinsot (1777 - 1859 AD) investigated the intersection of vertex figures and discovered the great dodecahedron and the great icosahedron.

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Glass Geometry
Hans Schepker
325 Breed Road
Harrisville, NH 03450
FAX 603.827.3115

-All artwork, images and designs in this site are
(C) Hans Schepker 2003, 2004, 2005
-All typos and other blunders are also mine 8(