The Uniform Polyhedra
Contents
Introduction
Uniform polyhedra consist of regular faces and congruent vertices.
Allowing for non-convex 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 CD-ROM.
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 ray-traced images on these pages were rendered with POV-ray, from
data computed with the program mentioned above, using a conversion program
from Mathematica graphics format to POV-ray input.
Programs and Images are Available!
The Mathematica programs to compute and render the polyhedra
are included on the CD-ROM that comes with The Mathematica
Programmer II. The book contains also high-resolution 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 high-resolution image and
geometrical information. The pages can be accessed in these ways:
-
A visual index (sensitive map)
of all 80 polyhedra
GIF-animations
of all polyhedra! See them spin about a symmetry axis for better
visualization. The animations are linked through the high-resolution 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 |