| Here are some alternate boards to play Hex on. This first one I call "Pex11" because the cells are all pentagons, and the tiling is number 11 on the list of all known classes of pentagon that tile the plane. The complete list can be found here. Of all the classes given, only two of them, 11 and 14, meet these criteria: * nowhere do more than three pentagons meet in a point. * the pattern is topologically distinct from a hexagonal grid. In a normal hex grid, each interior cell is adjacent to six other cells. In the type 11 pattern, half the interior cells are adjacent to five neighbors. and the other half are adjacent to seven. The pentagons are colored accordingly. |
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| This is Pex14. A third of the interior cells are adjacent to five neighbors, a third to six, and a third to seven. They are colored accordingly. For both these tilings, I tried to find a way to define the borders such that the resulting board would present the same challenge to both sides. In this respect, Pex11 is probably a better game than the Pex14 board. Pex11 satisfies these criteria: *The overall board shape appears symmetric. *All four border rows are the same length (12) *The minimum-length path connecting border rows is the same (10) The minimum-length path for Black on the Pex14 board is 8, but it's 11 for White. Either the board shape should be changed, or one or both Black border rows should be reduced in length. It's not clear by how much, though. Of course, the pie rule, or one-move equalization, is still recommended, to reduce the advantage of the first move. Perhaps Pex14 could be balanced by giving White the first move without a pie rule, but that may not be enough. |
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