Icosahedron shortest distance between centers
Given a regular icosahedron of unit edge length, find the shortest distance between the centers of two opposite faces. The path between the two centers has to lie on the surface of the icosahedron. If the distance is then find
The answer is 19.
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1 solution
The following .GIF animation illustrates the unfolding of the faces of the icosahedron. The last frame shows one possible way to compute the distance between the two centers using two congruent triangles.
d = ( 1 ) 2 + ( 3 4 ) 2 = 3 1 9 . Hence, 3 d 2 = 1 9