# Galvagni Figures & Reid Figures for Polyhops

*Polyhops* are Thomas Atkinson's figures made by joining squares in the
plane hopscotch grid.
They are used in Kate Jones's
Hopscotch puzzle.
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 with no holes.
Galvagni figures first appeared in Erich Friedman's
Math Magic
for November 2004.

Here are minimal known Galvagni figures and Reid figure for polyhops.
The black tiles have no solution.
The gray tiles have no known solution.

### Galvagni Figures

### Reid Figures

### Galvagni Figures

#### Hypersymmetric Variants

### Reid Figures

#### Hypersymmetric Variants

### Galvagni Figures

#### Hypersymmetric Variants

### Reid Figures

#### Hypersymmetric Variants

Last revised 2012-02-24.

Back to Galvagni Compatibility
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Polyform Compatibility
<
Polyform Curiosities

Col. George Sicherman
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