Here are a few great books where you can find the truth about polyhedra, polytopes and how to build them:
... and here are a few nice sites:
- "Regular Polytopes"
by H. S. M. Coxeter. This
is the book for people who want to understand regular polyhedra and
regular polytopes. If you want to go overboard, then get
"Regular Complex Polytopes".
- "The Symmetries of Things",
by John H. Conway, Heidi Burgiel and Chaim Goodman-Strauss.
This is a very fun, deep and extremely well-illustrated book on everything symmetric, with a very modern approach.
- Geometric Regular Polytopes, by Peter McMullen. A very theoretical approach
to polytopes. One of the highlights is the six new regular polychoron compounds that were discovered by the author in 2018.
- "The Fifty-Nine Icosahedra"
by H. S. M. Coxeter, P. du Val, H. Flather and J. F. Petrie. A charming little book on the
stellations of the Icosahedron.
- "Mathematical models",
by H. Martyn Cundy, A. P. Rollett. This is a very nice but inexpensive book that includes most of the paper models in my office,
and much besides polyhedra.
"Dual Models and
by Magnus Wenninger. These detail methods for building a
very large number of polyhedron and related models,
particularly uniform polyhedra.
"Zome Geometry: Hands-on Learning with Zome Models"
by George W. Hart. This is a very nice introduction to the
The most valuable resource for anyone in the first stages of learning any topic must surely be Wikipedia, one of the best things to happen in the Internet age. I link to it extensively in this page.
- David Richter's page, which includes a very nice
list of Zometool projects. A few of the models in my office
(600-cell, first stellation of the 120-cell and a couple of others) were
built following directly the instructions in these pages - I learned a lot building those models!
Most others were inspired by models that appear in these pages. A big Thank You to David for the very inspiring and
- Scott Vorthmann's vZome. This program allows one to make virtual Zometool models. This makes extremely difficult models feasible, and it has been used to prove that many geometric objects can be built in Zometool. A very cool program! Also, lots of interesting geometric objects are presented in the site, some of which I show here.
- Eusebeia 4-D visualization. This is very useful for figuring out how to build Zometool projections of the convex 4-D regular and uniform polychora.
- Nan Ma's star polytope page, which was inspired by, and complements, the previous page, which did not have the star polytopes.
I refer extensively to these two useful pages above.
- Uniform Polychora and Other Four Dimensional Shapes. This is an amazing site, which lists all known uniform polychora. If new ones are discovered, this is the place to look for them.
- George Hart's page. From his beautiful site and its links you may explore the whole polyhedral universe.