LEGO Spheres

When I built the snowman I did a lot of guesswork and learned a little about building balls out of LEGO. The technique I used was to create pixeled circles of various size and piling them up until the result looked something like a sphere. It was done mostly by eyeballing it. When I built the snowman head I made the mistake of using an odd diameter for the circles. While this was great for positioning the nose in the center of the face it used up most of my 3 and 1 length pieces. Even length LEGO pieces are considerably more common, and there are no 5 or 7 length pieces, so the odd diameter caused some problems. For the body I used even diameter circles. I'll let you figure out why you can't use both even and odd diameter circles in the same LEGO ball.

In 2005 I was thinking about building a more geometrically correct sphere. Single peg LEGO blocks are 20% taller than they are wide, so building a sphere as many block tall as it is wide would yield an oblong shape that's 20% too tall. The solution is to build the sphere 20% wider than it is tall. Certain whole number sizes fit this description. 5 X 6, 10 X 12, 15 X 18, and 20 X 24 are the four smallest. You'll notice that each one of these uses an even diameter. Perfect! I drew out circles for each even diameter between 4 and 24 and started building. Here are the results.

Blue Sphere - Radius 12

Red Sphere - Radius 9

Orange Sphere - Radius 6

Light Green Sphere - Radius 3