The outside hides the inside
Each piece shows 12 of the 96 squares on the finished cube. In every one of the 65.
Those 65 leave 51 seam patterns, up to the 48 symmetries of the box. Fourteen pairs are identical from every side. In all 14, the pieces are not even congruent. They differ in shape, and in most cases in surface area and cycle rank too.
No twin pair shares a seam pattern. The outside tells you apart exactly where the inside is the same, and hides you where it is not.
Two closed cubes can be built from pieces that are not the same shape, and look identical. Two cubes built from identical pieces always look different.
| Pair | Surface | Cycle rank | Shapes |
|---|
Dissection #3
Closed, the seams stay. Open it, and the piece changes. The numbers above change with it.