A polydom is formed by joining doms at hypotenuses, short legs, long legs, and half long legs. In particular a short leg may be joined to a half long leg.
The strong surround number of a polydom is the fewest number of copies of the polydom that can surround it strongly; that is, surrounding even its corners. The dom cells must be joined according to the rule given above.
Strong surround numbers for polyominoes were proposed by Jaime Poniachik in Issue 8 of Puzzle Fun. He asked for the smallest polyominoes with a given strong surround number. In Issue 10, Rodolfo Kurchan extended the problem to polyiamonds, polyhexes, and polyaboloes. He also investigated the smallest polyforms that cannot surround themselves, and the smallest holeless such polyforms. However, his results were not complete.
Here I show minimal known strong surrounds for the monodom and the didoms. These surrounds are not necessarily uniquely minimal. The numbers indicate how many tiles surround the central tile.
If you find a solution with fewer tiles, please write.
See also
Last revised 2026-06-09.