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Myers Polyhex Tiles

by Gelada, published

Myers Polyhex Tiles by Gelada Nov 19, 2009

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Summary

This shape is a world record holder you need 20 tiles before it will tile the plane periodically (10 up to symmetry). It fits together in an amazing variety of ways but can easily block itself. Making it a fun puzzle.

The tiles were found by a massive computer search by Joseph Myers. Look for this and other puzzling shapes at: http://www.srcf.ucam.org/~jsm28/tiling/

The idea to make physical tiles was originally from Chaim Goodman-Strauss: http://www.mathbun.com

Instructions

Cut out of acrylic/card/wood/stone using your favourite cutter, laser water-jet, craft etc. Cut file set up for A4 sheet.

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Hi! Thanks for this great idea. The file has a small error--not all the tiles are exactly the same shape. I think after the tiling was done, the whole thing got squashed a bit along one axis. With the material, size, and kerf I used, it turns out that the tiles don't fit in some orientations (well, not without applying a lot of force).

If you want the original file that doesn't have this issue, the link is available through the page you linked to: http://www.polyomino.org.uk/mathematics/polyform-tiling/http://www.polyomino.org.uk/ma...

And it is the anisohedral 16-hex, k=10, link is in the table in the polyhex section

Direct link to file: http://www.polyomino.org.uk/mathematics/polyform-tiling/16-hexe-10-aniso.ps.gzhttp://www.polyomino.org.uk/ma...

Hope that helps!

The stuff that can be made with this is amazing. Somebody needs to sell this idea to tile makers and brick makers. Can you imagine what a brick house or a tiled patio would look like using these patterns as paving tiles! No more plain brick homes. Every wall would be different. ABSOLUTELY AMAZING! I'm going to start cutting tiles ASAP for my back yard.

Personally I do like a nice brick pattern, so I am not going to follow you all the way. I do agree that Myers Tiles patio would be awesome. I look forward to seeing pictures!

The blue and red colors makes me think that this could also be a two-player game, like Hex.

What a great idea. A general tiling game. You alternate placing tiles. The winner is the last player to move. There's probably a winning strategy even in a tilable case like this but coule be fun...

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