  We give a complete solution to the extremal topological combinatorial problem
of finding the minimum number of tiles needed to construct a polyomino with $h$
holes. We denote this number by $g(h)$ and say that a polyomino is crystallized
if it has $h$ holes and $g(h)$ tiles. We analyze structural properties of
crystallized polyominoes and characterize their efficiency by a topological
isoperimetric inequality that relates minimum perimeter, the area of the holes,
and the structure of the dual graph of a polyomino. We also develop a new
dynamical method of creating sequences of polyominoes which is invariant with
respect to crystallization and efficient structure. Using this technique, we
prove that crystallized polyominoes with $h_l=(2^{2l}-1)/3$ holes are unique.
