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The tangram and Sei Shonagon Chie no Ita are popular dissection puzzlesconsisting of seven pieces. Each puzzle can be formed by identifying edges fromsixteen identical right isosceles triangles. It is known that the tangram canform 13 convex polygons. We show that Sei Shonagon Chie no Ita can form 16convex polygons, propose a new puzzle that can form 19, no 7 piece puzzle canform 20, and 11 pieces are necessary and sufficient to form all 20 polygonsformable by 16 identical isosceles right triangles. Finally, we examine thenumber of convex polygons formable by different quantities of these triangles.

The Convex Configurations of "Sei Shonagon Chie no Ita" and Other Dissection Puzzles