Using sophisticated computer searches, Edo Timmermans has discovered an enormous number of 8-piece dissections of a 3-cube, a 4-cube, and a 5-cube to a 6-cube. And as I discuss in my Chapter 21 updates, some of them make extremely fine puzzles, in which some pieces must be rotated relative to each other as you assemble the cubes. One remarkable set of dissections involves two pieces that cannot be separated from each other. The two pieces interlock in a way that allows them still to be moved somewhat relative to each other. Here is the level-by-level description of the 4-, 5-, and 6-cubes.
In the next photo, we see a wooden model that Edo crafted for this dissection. The two pieces that cannot be disentangled from each other (pieces S and X) appear in the center as they would be configured in the 6-cube. The 3-cube is piece Z, and going clockwise around the center starting from the 3-cube are pieces I, H, O, V, and A.
The interlocked pieces also appear together in the 5-cube. The limited movement allows one to reconfigure from the 6-cube to the 5-cube, as we see in the next few photos.
Isn't this model amazing!
Photos are used with the permission of Edo Timmermans.
All else is copyright 2005, Greg N. Frederickson.
Permission is granted to any purchaser of Dissections: Plane & Fancy to print out a copy of this page for his or her own personal use.
Last updated April 4, 2005.