The "long diameter" (widest part) of an
icosahedron may be calculated from the edge length of the icosahedron.
It turns out that the diameter is
times larger than the side length, where
is a constant called the "golden mean." Can the students derive this quantity (very hard, especially if the students aren't familiar with trigonometry!) or experimentally determine the quantity by measuring the diameters and edge lengths of several icosahedra?
Can the students calculate the surface area of the icosahedra? What about obtaining an estimate of volume? Estimating the radius of inscribed and circumscribed spheres may help the students provide an upper and lower bound on the volume.
Author: Frederick J. Wicklin <email@example.com>
Comments to: firstname.lastname@example.org
Created: Summer 1994 --- Last modified: Jul 21 1996
Copyright © 1994-1996 by The Geometry Center All rights reserved.