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You can take any of a variety of paths from the center to the edges alt text http://www.cflmath.com/%7Ereid/Polyomino/Images/9omino36_6x6.gif.

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Splitting a Polygon into Two Congruent Pieces Kimmo Eriksson The American Mathematical Monthly Vol. 103, No. 5 (May, 1996), pp. 393-400 It might be relevant for this problem and at least is an example of how to prove such things.

Samuel J. Maltby Trisecting a rectangle Journal of Combinatorial Theory, Series A Volume 66, Issue 1, April 1994, Pages 40-52

Polyominoes of order 3 do not exist I. N. Stewart and A. Wormstein Journal of Combinatorial Theory, Series A Volume 61, Issue 1, September 1992, Pages 130-136

You can take any of a variety of paths from the center to the edges:

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Comments

Splitting a Polygon into Two Congruent Pieces Kimmo Eriksson The American Mathematical Monthly Vol. 103, No. 5 (May, 1996), pp. 393-400 It might be relevant for this problem and at least is an example of how to prove such things.

Samuel J. Maltby Trisecting a rectangle Journal of Combinatorial Theory, Series A Volume 66, Issue 1, April 1994, Pages 40-52

Polyominoes of order 3 do not exist I. N. Stewart and A. Wormstein Journal of Combinatorial Theory, Series A Volume 61, Issue 1, September 1992, Pages 130-136

You can take any of a variety of paths from the center to the edges alt text http://www.math.ucf.edu/%7Ereid/Polyomino/Images/9omino36_6x6.gif.

You can take any of a variety of paths from the center to the edges alt text http://www.cflmath.com/%7Ereid/Polyomino/Images/9omino36_6x6.gif.

32 tiler http://img710.imageshack.us/img710/2788/tiler3.jpg