  We define the Helly number of a polyomino $P$ as the smallest number $h$ such
that the $h$-Helly property holds for the family of symmetric and translated
copies of $P$ on the integer grid. We prove the following: (i) the only
polyominoes with Helly number 2 are the rectangles, (ii) there does not exist
any polyomino with Helly number 3, (iii) there exist polyominoes of Helly
number $k$ for any $k\neq 1,3$.
