The Platonic Solids,The five perfect regular polyhedra each is
composed of the same regular polygons and each has the same number of faces meeting at each point. They are the icosahedron ,the dodecahedron, the cube, the octahedron and the tetrahedron.
The Archimedian SolidsThese are composed of different regular polygons but there must be the same arrangement of faces about each point. They can be generated from the platonics by slicing off the corners (truncating), expanding them and filling in the gaps with regular polyhedra and a transformation called the snub. There 13 of them.
The Catalan Solidsare a transformation of the Archimedians . Each point in the Archimedian is represented by a face which has an edge for each of the faces around the original point.
There are many other regular polyhedra. An antiprism, a pyramid, a prism and the associated Catalan solids are shown.
The following 2 links are to magnificent virtual reality sites. You do need to have a late version of netscape and plugin installed but the sites link you to the plugin download site and instructions.
Conway Notation for Polyhedra
The last link is to some supurb artwork and a feast of other links
The Pavilion of Polyhedreality
Inspired by this magnificence I have written Poly a dos program that can be used to study the truncations and transformations of the Platonic Solids. Poly will run on any machine that can emulate dos(most of them). It is available as either a zip or self-extracting .exe file.
There is also an on line version of poly. You need java to run it
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