The Uniform Polyhedra
Contents
Introduction
Uniform polyhedra consist of regular faces and congruent vertices.
Allowing for nonconvex faces and vertex figures, there are 75 such polyhedra,
as well as 2 infinite families of prisms and antiprisms. A recently discovered
uniform way of computing their vertex coordinates [Harel93] is the basis
for a program to display all of these solids, among which are many beautiful
and stunning shapes.
This text is an excerpt of Chapter 9 of R. Maeder's book The
Mathematica Programmer II. An expanded version of these Web pages can
also be found in the Mathematica notebook Polyhedra.ma
from the Illustrated Mathematics CDROM.
About the Images on These Pages
The metric properties and graphics data were computed with a Mathematica
program, developed by R. Maeder, based on a C program by Zvi Har'El.
The raytraced images on these pages were rendered with POVray, from
data computed with the program mentioned above, using a conversion program
from Mathematica graphics format to POVray input.
Programs and Images are Available!
The Mathematica programs to compute and render the polyhedra
are included on the CDROM that comes with The Mathematica
Programmer II. The book contains also highresolution color
images of all uniform polyhedra. Follow the link to the book's home page
for more information and direct ordering in association with amazon.com.
Volume 1 / Plate 6
Volume 2 / Plate 5
Volume 2 / Plate 6
cube
icosahedron
octahedron
tetrahedron
Graphic Resources
There is one page for each polyhedron with a highresolution image and
geometrical information. The pages can be accessed in these ways:

A visual index (sensitive map)
of all 80 polyhedra
GIFanimations
of all polyhedra! See them spin about a symmetry axis for better
visualization. The animations are linked through the highresolution images
on the individual polyhedra pages. The animations use a rather high number
of frames for smoother motion and are, therefore, quite large.
© 1998 MathConsult Dr. R. Mäder
http://www.mathconsult.ch/showroom/unipoly/INDEX.HTMl
Comments to webmaster@mathconsult.ch; Last update: 31.07.1998 