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"Four Corners" Cardstock Puzzle

All > Other > Toys > "Four Corners" Cardstock Puzzle by tsmaster

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When I was a kid, I had a puzzle made of six plastic pieces that assembled into a symmetrical four-pronged shape. Years later, I discovered that this puzzle was originally designed by Stuart Coffin, and went by the name "Four Corners" (amongst many others).

I've got a copy of Coffin's "Geometric Puzzle Design", which is a good reference and a good resource, but I had a hard time figuring out from the diagrams how the puzzle was formed - my geometric memory was a little hazy.

Coffin remarks that the puzzle can be made out of a few geometric primitives, but I couldn't get a good mental image of the actual shapes of the pieces.

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So, I fired up Milkshape 3d [http://chumbalum.swissquake.ch/index.html], an inexpensive 3d modeling tool that is designed for low-poly models. It also has "snap to grid" and "manual vertex placement" features, which would be useful later. I modeled the three separate primitives described by Coffin that together make a single puzzle piece. After I printed them out (see below), I fiddled with them until I figured out how they all went together. I then came back to Milkshape and recreated the complete puzzle piece as a single model (shown here).

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I then imported the OBJ file of my model into Pepakura Designer [http://www.tamasoft.co.jp/pepakura-en/], a tool that takes low-poly models and unfolds them into printable templates that you can cut out and assemble yourself. I fiddled a bit with it to get the "development" (the unfolded version) shown - the automatic version made some cuts that I didn't like.

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I printed out six copies of the puzzle piece onto cardstock, folded them into the weird "M" shapes here

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Three pieces go together in a sort of "rocketship" shape

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the other three pieces form a "nebula", if you like, and then by fitting the rocketship into the nebula, you form the completed puzzle. It's interesting to me - there are six pieces of the puzzle, and yet the final shape has tetrahedral symmetry. Clearly something about how 3-dimensional symmetries work out stymies my mental geometer - I can easily grasp how six pieces would form a 6-way symmetric pattern.

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