3 cubed + 4 cubed + 5 cubed = 6 cubed.

This little known fact is not related to Pythagoras' theorem; however it provides good opportunities for puzzle designs: - Build a single large cube using all the pieces from the 3 smaller cubes.

It is a nice challenge to find the minimum number of pieces required to make the puzzle solvable. Then repeat so that, in turn, the smallest, medium, & largest cube remains uncut.

 

This dissection is one that leaves leaves the smallest cube uncut, and was manufactured in mahogany by Pentangle for ICI (Imperial Chemical Industries) in 1984 .

 


This set of polycubes made of rosewood in oak boxes was designed and made by Japanese craftsman Sabu Oguru.

Each of the Polycube pieces is a stylised animal.

The 3-cubed box contains 7 animals.
The 4-cubed box contains 13 animals.
The 5-cubed box contains 25 animals.
or
The 6-cubed box contains all 45 animals.

At first sight it looks impossible that the contents of all 3 small boxes will fit into the big one. However it quickly becomes apparent that it is possible; however the solutions are elusive.

What this puzzle lacks by having so many pieces, it more than makes up for it by being such a charming "Noah's Ark" like of plaything.

     
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