Galvagni Figures for Polypents

A polypent is a figure made of regular pentagons joined edge to edge. 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.

Many of the polypent Galvagni figures up to order 5 were found by Scott Reynolds or Erich Friedman.

Here are minimal known Galvagni figures for polypents. The black tiles have no Galvagni figures. The gray tiles have no known Galvagni figures.





Hypersymmetric Variants


Hypersymmetric Variants

Joint Solutions

No hypersymmetric variant is known for the V and Z pentapents. The X pentapent has no solution at all. We can make quasi-Galvagni Figures by pairing them:


Two to four tiles

Five tiles

Six or more tiles


Hypersymmetric Variants

Last revised 2023-03-31.

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Col. George Sicherman [ HOME | MAIL ]