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Subject: Pex rss

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David Bush
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Lexington
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Pex is Hex with pentagons instead of hexagons. It is available to play, along with Hex and several other connection games, on the iGoogle Game Center gadget.



This pattern was taken from the list of the 14 known plane tilings by congruent convex pentagons. http://www.mathpuzzle.com/tilepent.html Two criteria had to be met:

* Nowhere should more than three edges meet at a single vertex.
* The tessellation should be topologically distinct from a beehive grid; in other words, not all the interior cells should be adjacent to six neighbors.


Patterns 11 and 14 were the only ones that met both criteria. Pattern 14 has an asymmetry to it which makes it difficult to define the borders of the playing area in a fair way. So, I chose pattern 11. The interior green cells have five neighbors and the yellow ones have seven. With the pie rule a.k.a. the swap rule in place, a balanced game is assured. Pattern 11 was discovered by Marjorie Rice.

I'm not sure if Pex deserves its own page. Arty Sandler, who runs the Game Center server, submitted it. It was accepted, so I will add some content. I'm making a high resolution image file for those who wish to print out their own board. I'm not sure where you could get oblong tokens. I will also add a session report for the game which produced the position shown above.
 
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