Uniform Polychora Project
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The Uniform Polychora Project in geometry is a collaborative effort to recognize and standardize terms used to describe objects in higher-dimensional spaces. The project aims: to collect information about uniform polychora as well as information about uniform polytopes in dimensions higher than 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 Horton Conway and Michael Guy established by computer analysis in the mid 1960s that there are 64 convex nonprismatic uniform polychora. 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 1849 uniform polychora outside the infinite families of prismatic polychora. (Before the Project adopted a stricter definition of uniform polychoron in 2005, the total was 8190.) As to be expected, less is known about uniform polytopes in the higher spatial dimensions.
Many of the terms for polychora were recently coined 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)
