The '''Uniform Polychora Project''' in [[geometry]] is a collaborative effort to recognize and standardize terms used to describe objects in [[higher-dimensional space]]s. The project aims: to collect information about [[uniform polychora]] as well as information about [[uniform polytope]]s in dimension ≥ 4.; to enumerate the shapes; and eventually to make a complete list. Standard extensions and generalizations of terms and definitions allow a common vocabulary, and precise communication when necessary. While names for [[polychora]] are not entirely rigorous, the creation of formal or abstract names is highly desirable. Major contributors are [[Jonathan Bowers]], [[Norman Johnson]] and [[George Olshevsky]].
[[John Conway]] and [[Michael Guy]] established by computer analysis 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]]. The convex uniform polychora are listed at George Olshevsky's Uniform Polychora website
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 which are [[convex uniform polychora]] with the other 8126 being [[nonconvex uniform polychora]]. As to be expected, less is known about uniform polytopes in the higher spatial dimensions.
Many of the terms for polychora were recently created by the principal Project researchers.
Terms include:
* [[Glome]]
* [[Hyperball]]
* [[Hypercircle]]
* [[Hypercube]]
* [[Hyperplane]]
* [[Hypersphere]]
* [[Hyperspherical simplex]]
* [[Icositetrachoron]]
* [[Small ditrigonary icosidodecahedral antiprism]] (Jonathan Bowers’s name is [[sidtidap]])
==External links==
*[http://members.aol.com/Polycell/glossary.html Glossary for Hyperspace]
[[Category:Polytopes]]
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