Galvagni Figures & Reid Figures for Polycairos

A cairo is a pentagon with at least four sides equal and forming two nonconsecutive right angles. A polycairo is a plane figure formed by joining cairos edge to edge on the polycairo grid. A Galvagni figure is a figure that can be tiled by a polyform in more than one way—a kind of self-compatibility figure. A Reid figure is a Galvagni figure without holes. Galvagni figures and Reid figures first appeared in Erich Friedman's Math Magic for November 2004.

Here are minimal known Galvagni figures for polycairos.

Monocairo

Impossible

Dicairos

Impossible

Tricairos

Impossible

Tetracairos

Impossible

Mirror Variants

Pentacairos

Impossible

Reid Figures

Last revised 2013-10-15.


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Col. George Sicherman [ HOME | MAIL ]