# Galvagni Figures & Reid Figures for Pentominoes

A *pentomino* is a figure made of five squares 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.
A *Reid figure* is a Galvagni figure without holes.
Most of the pentomino Galvagni and Reid figures were found by
Erich Friedman
of Stetson University
and Michael
Reid of the University of Central Florida.
Corey Plover found the minimal Galvagni figure for the T pentomino.

Here are minimal known Galvagni figures for pentominoes.
See also
Galvagni Figures & Reid Figures for Hexominoes,
Galvagni Figures & Reid Figures for Heptominoes,
and
Galvagni Figures & Reid Figures for Octominoes.

And here are minimal known Reid figures:

Here is an orthogonally symmetric variant for the W pentomino:

Here are diagonally symmetric variants for the F, L, N, P, and Y pentominoes:

Here is a birotarily symmetric variant for the F pentomino:

## Biased Pentominoes

Biased pentominoes may be reflected diagonally and rotated
180° but not 90°.
For a discussion of restricted-motion polyominoes, see
Alexandre Owen Muñiz's A Polyformist's Toolkit.

Last revised 2014-10-09.

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Col. George Sicherman
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