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.

Monohop

Dihops

Trihops

Galvagni Figures

Reid Figures

Tetrahops

Galvagni Figures

Hypersymmetric Variants

Reid Figures

Hypersymmetric Variants

Pentahops

Galvagni Figures

Hypersymmetric Variants

Reid Figures

Hypersymmetric Variants

Last revised 2012-02-24.


Back to Galvagni Compatibility.
Back to Polyform Compatibility.
Back to Polyform Curiosities.
Col. George Sicherman [ HOME | MAIL ]