The '''Uniform Polychora Project''' is a collaborative effort to recognize and standardize terms that geometers can use to describe objects in [[higher-dimensional spaces]]. The project aims to collect information about [[uniform polychora]] as well as information about [[uniform polytope]]s in higher order (greater than four)dimensional spaces. The project aims to enumerating the shapes and eventually enumerate a complete list.
[[John Horton Conway]] and [[Michael Guy]] established that there are 64 [[convex polychora|convex]] [[nonprismatic polychora| nonprismatic]] [[uniform polychora]] in the mid-1960s. [[Thorold Gosset]] completely enumerated the [[convex uniform polytopes with regular facets]].
While these names for [[Polychora]] are not entirely rigorous, the creation of formal or abstract names is highly desirable. Standard extensions and generalizations of these terms and these definitions allows formal mathematicians and interested others a common vocabulary, and allows communication to be precise when necessary.
A large amount of the work being done on this project is done by [[Jonathan Bowers]], [[Norman Johnson]] and [[George Olshevsky]].
The vast majority of the [[uniform polychora]] were discovered by Bowers, with the '''Uniform Polychora Project''' finding the rest for a total of 8190 uniform polychora outside the infinite families of prismatic polychora. There are only 64 are [[convex uniform polychora]] with the other 8126 as [[nonconvex uniform polychora]]. As to be expected, the less is known about uniform polytopes in the higher spatial dimensions.
The convex uniform polychora are listed at [[George Olshevsky]]'s Uniform Polychora website.
A computer analysis counting all the [[convex polyhedra]] under the speicific constraints which actually give rise to convex uniform polychora (by [[John Horton Conway]] and [[Michael Guy]]) established in the mid-1960s that there were only 64 convex nonprismatic uniform polychora.
Many of the terms for polychora were recently created by one of the priniciple researchers in the Uniform Polychora Project. According to the [http://members.aol.com/Polycell/glossary.html Glossary for Hyperspace], use of the terminology as set forth herein for mathematical discourse and publication is, of course, strongly encouraged.
Some of these terms (not all developed by the Uniform Polychora Project) include:
* [[Glome]]
* [[Hyperball]]
* [[Hypercircle]]
* [[Hypercube]]
* [[Hyperplane]]
* [[Hypersphere]]
* [[Hyperspherical simplex]]
* [[Icositetrachoron]]
* [[small ditrigonary icosidodecahedral antiprism]](Jonathan Bowers’s name: [[sidtidap]])
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http://members.aol.com/Polycell/glossary.html
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