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 <fjw@geom.umn.edu>

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Created: Summer 1994 ---
Last modified: Jul 21 1996

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