Take the 2-minute tour ×  Imagine that I have a truncated
icosahedron consisted of 60 vertices, each of degree $deg(v) =
3$, and fixed edge length $L$. I'd like to assign some constant
curvature or bending angle $\theta$ to each edge s.t. I can
deform the icosahedron into its circumscribing sphere.  As a
function of the edge length $L$, what value of $\theta$ allows
me to properly perform this deformation?  share|improve this
question I don't understand how you're using the "bending angle"
to deform the icosahedron. Are you looking for the angle
$\theta$ that each edge makes with the circumscribing sphere? – 
anon Jul 17 '11 at 23:49 @anon, sorry for the confusion! No I'm
looking for the bending angle that places each edge on the
surface of the sphere. –  R.H. Jul 18 '11 at 3:04 Oh, you mean
the angle formed by the arc which results from a radial
projection of an edge onto the circumscribing sphere. –  anon
Jul 19 '11 at 12:15 add comment  1 Answer  up vote 2 down vote
accepted  Fix $L=1$. Then the radius of