PPT Slide
There are three angles to be concerned with intially:
1) slant angle of each face to the central plane: alpha
(set to 60 degrees initially to approximated an icosahedron)
2) base (corner) angle of each face: beta (or miter) angle.
3) angle that the edges of the faces must be cut to so
Assuming we set angle (1) (alpha) to 60 degrees,
for a five sided figure we can calculate the other two angles as follows:
psi = 180/pi * ArcCos(Sin(Pi/5)*Sin(60*pi/180))
beta = 180/pi * ArcTan(1/(Cos(60*pi/180)*Tan(Pi/5)))