Galvagni Figures for Polylines

A right polyline (or square polyedge, or (2,1)-polyominoid) is a plane figure made of equal line segments joined end to end at straight or right angles. A Galvagni figure is a figure that can be tiled by a polyform in more than one way—a kind of self-compatibility figure. Galvagni figures first appeared in Erich Friedman's Math Magic for November 2004. Galvagni figures for polylines first appeared in Math Magic for August 2006.

Here are minimal known Galvagni figures for polylines. The gray polylines are unsolved. The black polylines have no Galvagni figures.

Monoline

Dilines

Trilines

Tetralines

Without Crossings

Pentalines

Without Crossings

Last revised 2009-11-07.


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Col. George Sicherman [ HOME | MAIL ]