Geodesic Dome Mathematics

Hugh Kenner
Geodesic Math and How To Use It
Berkeley: University of California Press, 1976
ISBN: 0-520-02924-0.   Hardback. Out of print.
ISBN: 0-520-03054-0.   Paperback. Out of print.

This book contains the formulas for calculating Class 1 and Class 2 geodesic domes.


Xdome Package

The xdome package, in the ibiblio.org Linux archive, is a series of X Windows programs based on the math in Kenner's book, cited above. It is a rewrite of the gcdome package. xdome also includes a batch program to calculate strut lengths and their locations on a geodesic dome of any size and model.


Debian Dome Package

The dome package, available at the Debian website, is a C++ batch program that produces a list of vertices and struts in a geodesic dome or a geodesic parabolic dish, as input to a graphics program, like a Povray rendering program.


Great Circle Mathematics

The formula for the great circle calculation in gcdome came from:

Aviation Formulary V1.25
by Ed Williams     (e-mail address)
Last update: 9/29/1999


Other mathematic constants and formulae come from any mathematical handbook. gcdome used CRC Standard Mathematical Tables, The Chemical Rubber Company. Samuel L. Selby, editor.

This handbook contains the radius of an icosahedron based on its side, and useful properties of a pentagon. These properties are useful for calculating the maximum vertex angle theta of a meridian, 63.4349 degrees from north, when phi = 0 or 72 degrees east.


gcdome results approximate a Class 1 Icosahedron geodesic dome.

Here is a comparison of gcdome and a Class 1 Icosahedron dome at a frequency of 32 and a radius of 100:

Chord Length gcdome Class 1 Icosahedron
Number of chords 1584 1584
Minimum 3.32559 2.84331
Maximum 4.79520 4.13379
Mean 3.77408 3.75019
Stdev 0.28290 0.27784


Graphics

Tara's Desert Domes

R. Kowalczuk: Geodesic Domes, Beauty of Unsquared World

Richard Hawkins' Digital Archive: Synergetic Geometry and Miscellaneous


Table of Contents     Introduction     Models     How to Use Gcdome
Gcdome Examples     Copying