Back when I first started sewing geometrical footbags, one thing I loved about it was that to create a round sphere, all the panels used were cut in straight lines. I eventually applied those same geometrical spherical designs to some woodworking projects.
A little over 20 years ago I made this mahogany lamp in the shape of a truncated icosahedron -- the typical shape of a soccer ball. It contains 12 pentagons and 20 hexagons. It has 90 edges between the shapes, and therefore 90 connecting dowels.
Each pentagon and hexagon piece is cut from a slab of mahogany into either a pentagon or hexagon block. The edges are then beveled (this is also called an "ease over") and the block is sanded and waxed.
That's the easy part.
The hard part comes in when you go to assemble these blocks into the overall spherical shape. As you can see, I connected each block (pentagon or hexagon) with a total of 90 wooden dowels. But the angles at which these dowels need to enter each block, on both sides, are critical. If one angle is off even slightly, the blocks won't fit together right to make a sphere.
At the time I made this lamp I consulted with a university math professor in Copenhagen. He first calculated the dowel angles for the pentagons, then went through another process to calculate the dowel angles for the hexagons. It took him the better part of a weekend to calculate these angles for me!
Above is a smaller truncated icosahdron I made with lignum vitae wood. It's more dense than ebony, they used to say 'a wood so dense it doesn't float.' It's also very oily wood and was used in ship building because its oils protected it from damaging salt water. This sphere is about six inches in diameter.
The mahogany lamp, about a foot in diameter, casts a great splash of angled light on the wall and it's a focal piece in any room.
All images above are original photographs taken by 
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