The Lambada Cube - Harold Cataquet by Wayne Daniel - Interlocking Puzzles

I was fortunate to have acquired this awesome puzzle recently and it’s of course incredibly well made by Wayne Daniel.

Here’s an excerpt from Harold’s pamphlet that accompanied this puzzle:

“For this year's exchange, I decided to make a 3D version of my exchange puzzle for IPP #16. 

At the outset, you have five puzzles to solve: 3x3x4, 3x3×6, 3×4×4, 3×4×5, and 4x4×4. The 3x3x6 box has two solutions; the others solutions are unique. However, in playing with the pieces, I found many more shapes were possible, and these offered greater challenges. For example, take the 3x3x4 box and add one cube at each corner of one of the 3×4 faces. You now have what I call the toy box. This too has a unique solution.

Finally, a few thanks. As always, thanks to Bill Cutler for his BCPBOX program. It was invaluable in helping me design and solve "The Lambada Cube". 

Thanks also to Trevor Wood for his comments on an earlier version of "The Lambada Cube". And, lastly, a special thanks to Wayne Daniel and all the great people at "Interlocking Puzzles". 

I am sure that you will agree that they did a wonderful job in producing "The Lambada Cube". In fact, in looking at the sample cube they sent me, it dawned on me that there was another tetracube that I could have used in my analysis: the planar L-shape. I had a great panic that this tetracube would have been a better choice (in that it would yield better packings), so I went back to square one and started the analysis all over again with this new tetracube. Fortunately, it turned out to have too many solutions to the 4x4×4 cube (and many other boxes), so I rejected it. But, for a while there, I was worried that I'd have to redesign the cube.

I had lots of fun designing and playing around with the Lambada Cube, and I hope you will enjoy playing with it as much as I do. PLEASE don't just take this puzzle and put it on a shelf along with your other cubes!”