Ξ at the the 360 blog just posted a neat LEGO fact: it is possible to snap together two 2×4 lego bricks in 24 different ways. Given six of these LEGOs it is possible to snap them together in 915,103,765 different ways!
This inspired me to post a link to a cool website by Andrew Lipson. I show my topology class this website every time I teach the course. Lipson has created many beautiful mathematical sculptures out of LEGOs. Examples include the Möbius band (with little men walking on it!),
a Klein bottle (that is hinged so you can see that it is formed from two Möbius bands),
and a figure eight knot.