One shape, two cubes
53 shapes build 65 dissections. Twelve shapes each build two cubes that no rotation of the cube carries into one another. The piece does not determine the cutting.
In the flat puzzle it does. Through order 7, no Yemeni polyomino has two inequivalent embeddings. The extra room in three dimensions breaks that.
For seven of the twelve, the two pieces are the same by a proper rotation. One set of eight printed pieces builds both cubes. For the other five, the pieces are mirrors. A printed set of one cannot build the other.
Three of the rotation pairs also come apart: #8 and #24, #25 and #44, #53 and #57. Those three can be shown with a physical set. The seams on the outside differ, so you can tell the cubes apart without taking them apart. No twin pair shares a seam pattern.
| Pair | Relation | One printed set builds both? | Also comes apart |
|---|
Dissection #25
The camera does not reset. Watch the seams.