Photos of one of Edo Timmermans' cardboard models,
which I referred to in Chapter 21 updates to
Dissections: Plane & Fancy, by Greg N. Frederickson:

Edo Timmermans informed me that he had found 8-piece solutions for parallelopipeds for 3³ + 4³ + 5³ = 6³, for one of which he had made a cardboard model which he demonstrated at the Dutch Cube Day in 2004. First is his photo of all eight pieces:

Next is his photo of the 5-parallelopiped (with one piece pulled out) on the left, the two pieces for the 4-parallelopiped in the center, and the single piece comprising the 3-parallelopiped on the right:

Finally, he assembled the 6-parallelopiped except for the single piece that is the 3-parallelopiped, which he turned over to demonstrate that it wouldn't fit properly if it were oriented differently:

Even with the color-coding of parallel sides, it was challenging, using only the photos, to identify the exact shape of the pieces and how they fit together exactly. Edo then sent me the level-by-level diagrams below.

Once I had the above description, things became clear. In particular, Edo's dissection is translational! Note first that each piece is in the same orientation in each of the two figures in which it appears. Second, it is possible to assemble and disassemble the parallelopipeds without any rotation. For disassembly:

For the 4-parallelopiped, slide piece H off to the north northeast.

For the 5-parallelopiped (assuming the top surface is the leftmost of its levels):

• Slide piece S out through the top surface.
• Slide pieces A and I to the north northeast by 1 unit.
• Slide piece A off to the east.
• Slide piece X out through the top surface.
• Slide piece I off to the east.

For the 6-parallelopiped:

• Slide piece Z off to the east.
• Slide piece H off to the north northeast.
• Slide piece A off to the north northeast.
• Slide piece O off to the north northeast.
• Slide piece S out through the top surface.
• Slide piece X out through the top surface.
• Slide piece V down through the bottom surface by 1 unit.
• Slide piece I off to the east.

Photos and the diagram 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 March 19, 2005.