Uniform Polychora Project

The Uniform Polychora Project is a collaborative effort in geometry 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 4 dimensions and higher;
# Enumerate the shapes;
# Eventually 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.

The major contributors to this project are Jonathan Bowers, Norman Johnson and George Olshevsky.

History

In the min 1960's, John Horton Conway and Michael Guy established by computer analysis that there are 64 convex non-prismatic 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 Jonathan 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.) Less is known about uniform polytopes in higher dimensions.

Many of the terms for polychora were recently coined by the principal Project researchers.

Terms used by the Project include:
* Glome
* Hyperball
* Hypercircle
* Hypercube
* Hyperplane
* Hypersphere
* Hyperspherical simplex
* Icositetrachoron
* Small ditrigonary icosidodecahedral antiprism (Jonathan Bowers’s name is sidtidap)

External links

* [http://www.polytope.net/hedrondude/polychora.htm Uniform Polychora (Jonathan Bowers)]
* [http://members.aol.com/Polycell/uniform.html List of convex uniform polychora (George Olshevsky)]
* [http://members.aol.com/Polycell/glossary.html Multidimensional Glossary (George Olshevsky)]