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Dissections of Convex Figures
Michael Reid has a
site devoted to Rectifiable Polyominoes. More polyomino rectangles
are at Torsten
Sillke's site. For the Math
Magic problem of the month, Erich Friedman asks about n-convex
figures. All of this has lead me to wonder about something I'll call
Nontrivial Convexity. The following three figures display nontrivial
convexity. The first two are by Ed Pegg Jr (me), the third is by
Karl Scherer, courtesy of Michael Reid.
In a convex figure, if you pick any two points, the points between them are also a part of the figure. A figure without this property is nonconvex.
Trivial examples display simple rotational or translational symmetry.
For more examples of this, visit Doris
Schattschneider's Tiling site. These trivial examples of attaining
convexity are easy to find.
I'm interested in the Nontrivial examples, such as the following.
There is a related class of quadrilaterals which are 8-vex. I've made an interactive applet based on the above figures. I'd love to see more examples of non-trivial n-vex figures. Send answers.