game-1.png copyright 08/18/2002 Wendy Krieger

I suggested the tyler-game as a way of passing time in a Gardner-esque way. The idea is to see how many polygons one can crowd into an enclosure of the same size. The example on the left is shown for the enneagon 9.

The rules are as follows.

1. The centres of the polygons that form the enclosure must form a convex shape, with no three in line.
2. Every polygon must share an edge (ie two verticies and the edge between them) with at least one other polygon.
3. It must be possible to go from any polygon to any other, by only crossing shared edges. You can use the polygons in the enclosure in this rule.

Once we explored this, the tyler-game in hyperbolic space proves to be also interesting. The example shows an enclosure with a tyler-setting of 5,5,20. Note the arch of three pentagons pointing to 3 o'clock crosses the enclosure.

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