Small Rhombicosidodecahedron

Name of Model: ZPD Ball

Created by: 1brick

Found at: http://www.flickr.com/photos/1brick/sets/72157623223643559/

Details: LEGO geometry is deceptive. So many people assume that the LEGO world is boxy, a sort of 3-D pixelated reality. Of course, we can easily break out of that by using specialized elements or hinges, and LEGO proportions aren't actually square (a standard 1x1 brick actually has a 5:6 ratio of width to height) - but this post isn't about the geometry of LEGO parts. Sometimes you just want to use LEGO to show off other geometric shapes (you never know when an unusual shape will come in handy, but there's no need to have a model in mind when experimenting). I've previously blogged about some simple LEGO polyhedra before, but never anything as complex as today's model - today's pick is one that you've probably never heard about (and are unlikely to hear about in the future) in a school geometry class. This is a perfect small rhombicosidodecahedron. The technique is similar to the one used for simpler shapes - which means that this polyhedron is actually easier to build than to pronounce. Lest you think this is easy, check out the full Wolfram Alpha list of 62-faced polyhedra. Leave it to irregular polyhedra to make it difficult to blog about LEGO.

Pentominoes

Name of Model: pentominoes

Created by: retracile

Found at: http://www.flickr.com/photos/retracile/tags/pentominoes/

Details: An elegant game of pentominoes, complete with box. The size is a bit hard to grasp, but each cube is based on the size of a 2x2 tile (the 1/3rd height elements that are flat on top). Using the 6:5 ratio of LEGO brick dimensions, you get the 2 stud measurement vertically using one brick and two 1/3 elements (either tiles or plates).

Polyhedra

Name of Model: Platonic solids

Created by: OptimalControl

Found at: http://www.flickr.com/photos/optimalcontrol/3984102878/

Details: This is a beautiful collection of polyhedra that you can build if you have enough hinges. That is a mighty big if, but these do look great - good enough to justify buying the parts specifically through Bricklink or LEGO's online Pick a Brick to give it a shot (well, for the geometry teachers out there, anyways). The technique's not too complicated, but the execution is perfect.

Klein Bottle

Name of Model: Klein Bottle

Created by: Andrew Lipson

Found at: http://www.andrewlipson.com/kleinbottle.htm

Details: This is a LEGO sculpture of a Klein bottle made by the legendary knot theorist Andrew Lipson. OK, fine, he's actually legendary for his Escher-related LEGO models (Previously featured here). Complete LDRAW format building instructions are available for those of you who want to try this one at home. There are more pictures on this model's page as well. Take a close look at this one - I promise, it really is fascinating once you realize just what a Klein bottle is.

This is Wednesday's model of the day.