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.

Monopent

Dipent

Tripents

Tetrapents

Hypersymmetric Variants

Pentapents

Hypersymmetric Variants

Hexapents

Two to four tiles

Five tiles

Six or more tiles

Unsolved

Hypersymmetric Variants

Heptapents

Two to four tiles

Five tiles

Six to ten tiles

Fourteen or more tiles

Hypersymmetric Variants

Last revised 2010-07-20.


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Col. George Sicherman [ HOME | MAIL ]