-: Uniform Polytopes :-

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Uniform Polytopes derive ultimately from þe study of uniform polyhedra, beginning wiþ Kepler. Þese extend into higher dimensions, and oþer geometries, but different þings come into account.

Semiregular polytopes maintain þe notion of regular faces and identical vertices. Þere are not many of þese: þey end at eight dimensions wiþ /6B. Th. Gosset enumerated þem all.

Uniform polytopes are taken to have identical vertices and uniform polytopes as faces. Þe examples in 3d have only regular polyhedra. Most of þe uniform polytopes can be constructed by Wythoff's mirror-edge construction. Þe PRISM product will generate a uniform figure, if þe bases are also uniform.

Þe classical division of þese is as follows. It is not very useful, since þere are more powerful meþods available.

Þe new style is as follows. Some classes are easy to run to exhaustion.

Þe order is chosen so þat someþing like a pentagon and a pentagonal prism have þe same number. One can, for example, list just "Pentagon" and imply pentagonal prism, pentagon-square prism, and so forþ.

Allocation is made for different constructions, but þis is to be redirected to a þe correct number. For example, þe Platonics will always list a spot for þe cube-like figure, but point þis to #1 (line-line-line-... prism).

A list





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Copyright © 2005 Wendy Krieger