[net.math] Icosahedron Vertices

TOPAZ:shallit@ucbvax.UUCP (07/05/83)

~h
Does anybody know how to compute the XYZ co-ordinates of the
vertices of a regular (Platonic) dodecahedron or icosahedron? 
Pointers to references in the literature would also be welcome.

ellis@flairvax.UUCP (Michael Ellis) (07/11/83)

    If I'm not mistaken, these twelve points in threespace should make
    a really swell icosahedron:

	(+-t, 0,   +-1)
	(+-1, +-t, 0)
	(0,   +-1, +-t)

    ...where "+-" means "plus or minus" (so each parenthesized glorb
    represents four points) and "t" is "tau" (damn barbarian keyboards
    got no greek letters) which is the thoroughly cosmic "golden mean":

	t = (1 + sqrt(5)) / 2

    There are so many "coincidences" involving this number that
    further discussion would belong in net.religion. We could really
    clean up that newsgroup, you know.

    Michael Ellis - Fairchild AI Lab - Palo Alto CA - (415) 321-0990

ljdickey@watmath.UUCP (Lee Dickey) (07/12/83)

I think that you will find equations for your vertices in the book
"Regular Polytopes" by H.S.M. Coxeter, Published by Dover Publications, Inc.
in 1973.  You should look at pages 15 to 24.
 
-- 
                lee dickey

                           Lee Dickey
                           University of Waterloo
                           ...{decvax|allegra}!watmath!ljdickey
                           ljdickey@watmath.UUCP