Studies into Polyhedra - Sources

Look around the Graphics Lab

Regular, Semi-Regular Polyhedra, and thier Duals (first page)
Prisms, Anti-prisms, Pryamids, and related Polyhedra
Miscellanous Polyhedra: Deltahedra
Johnson Solids -- The other convex polyhedra with regular faces

Why I studied polyhedra, and Image Generation Techniques
Known Polyhedral Mathematical Formula
Data Sources and links for Polyhedral Data

Data Sources for Polyhedra

Whenever possible I used Exact Mathematics to generate the "OFF" file data for the polyhedral images I generate. (See Mathematical Formula). However I have only a few of the formulas for this.

One of the best sources I found was George Hart's Encyclopedia of Polyhedra. This however only listed the polyhedra in a VRML (suffix ".wrl") format. However a simple Perl Script I wrote extracted the data and face data to "OFF" data format. His naming has some faults, particularly the use of the term "trapezoidal" and "trapezohedron" for polyhedra with kite shaped faces, which are not "trapezoids" at all. See definition for a Trapezoid.

A Second good source of data was the NetLib Polyhedron Database, numbered as per the "Holt Polyhedral Library". This database used their own "poly" data format, which contained not only 3D data but 2D "nets" of the polyhedron. The data was easily converted to the "OFF" file format, for my own use. The Polyhedral Database also has some serious faults. First the 3D object data for Archimedian Polyhedra is completely missing from the source files. Then for 5 of the Johnson Solids not all the faces are listed. Finally for 2 Johnson Solids, the 3D object data was completely wrong!

For my own raw OFF datafiles (which I publish with the object) I use Exact Mathematics where possible, then the Polyhedron Database and failing that George Hart's less accurate VRML data. Generally I also rotated the object so as to match the orthogonal axises as as closely as I could. This makes it easier to later position OFF data for various uses later.

A lot of polyhedra has also now been included into Wikipedia, particularly the polyhedra groups such as, Polyhedra, Archimedean, Catalan, Deltahedron, Prism, Antiprism, Bipyramid, Trapezohedron.

Of course there are lots of other types of polyhedra I have not even looked at, for example Zonohedron with two extra polyhedra (at the end of the list given), and Waterman Polyhedron which are generated from sphere filling convex hulls.


WARNING: Many of the sources are no longer available. Though I am sure an equal number of new sources are now online, I have not searched for them, but should be easy to find via a web search engine.

Created: 25 Sepember 2003
Updated: 28 January 2009
Author: Anthony Thyssen, <>