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By George Hart for the Museum of Mathematics

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Polygons with finger joints can be friction-fit together to make many kinds of structures, including tessellations and polyhedra. But one never has enough parts for larger and larger projects, so Steve Garrison makes his own from wood. This ball comprises 60 squares, 20 triangles, and 12 pentagons, with 30 rhombic openings.

Working just in the plane, pentagon cycles close into ten-sided polygons which can overlap nicely. This pentagon tiling derives from explorations by the astronomer Kepler.

It may be surprising what structures you can make with just squares, if you have enough.

The basic unit in the above structure comes about by imagining space packed with rhombic dodecahedra, then separating each from its neighbors with rhombic prisms as connectors, and building just the square faces of the prisms. Equivalently, one could start with the dual packing of octahedra and tetrahedra, expand it with triangular prisms, and build just the square faces of the prisms.

More:
See all of George Hart’s Math Monday columns

Gareth Branwyn

Gareth Branwyn

Gareth Branwyn is a freelancer writer and the former Editorial Director of Maker Media. He is the author or editor of over a dozen books on technology, DIY, and geek culture. He is currently a contributor for Boing Boing and WINK Books. And he has a new best-of writing collection and “lazy man’s memoir,” called Borg Like Me.


  • http://pulse.yahoo.com/_XZEOIRTH2TDUPTURYNPUOQZWLM Jeff

    Heh, those look like Zaks.  Does anyone remember those??

  • http://pulse.yahoo.com/_XZEOIRTH2TDUPTURYNPUOQZWLM Jeff

    Heh, those look like Zaks.  Does anyone remember those??

  • http://twitter.com/gavinskio Gavin Crosby

    @18saughtonmains – even more suitable for your maths learners – maths and woodwork http://t.co/Whoo1wy

  • http://twitter.com/Rbotguy Jeff Kroll

    If you can cast a silicone mold, here’s an easier way…
    http://www.shapeways.com/forum/index.php?t=msg&th=5260
    http://www.shapeways.com/shops/robotguy
    Still tweaking the snap-fit interface, but definitely useable.

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  • Anonymous

    I just paíd $20.87 for an íPad 2.64GB and my Girlfriend loves his Panasoníc Lumíx GF 1 Cámera that we got for $38.79 there arriving tomorrow by UP S.I will never pay such expensive retail príces in stores again. Especially when I also sold a 40 inch LCD T V to my boss for $657 which only cost me $62.81 to buy.
    Here is the website we use to get it all from : http://BidsBit.com