# 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.

### Impossible

### Impossible

### Impossible

### Impossible

### Mirror Variants

### Impossible

### Reid Figures

### Mirror Variants

Last revised 2023-08-10.

Back to Galvagni Compatibility
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Polyform Compatibility
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Polyform Curiosities

Col. George Sicherman
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