I have always loved spheres. There is an incredible beauty in an object that is perfectly round. A sphere cut in any direction makes a circle. A sphere is an infinite collection of circles.

This sphere starts as an Icosahedron. Each face triangle is divided as shown on the right. Every intersecting line creates a new vertex. The vertices are then pushed out to an imaginary sphere, so that each point is the same distance from the center. Applying a little math the angles and the length of the lines are easily calculated.
I recommend picking up this book for more information on the math involved.

360 pieces of mat board were cut, sanded and painted before assembly. Total assembly took over 40 hours which included making a jig to cut the mat board. On a future project the jig would be replaced with a better designed method for cutting the struts.