Strong Surround Numbers for Polyrafters

In combinatorial geometry, a drafter is a plane figure formed by bisecting an equilateral triangle by an apothem. The term is due to Ed Pegg.

A polydrafter is formed by joining drafters at short legs, long legs, hypotenuses and half hypotenuses. In particular a short leg may be joined to a half hypotenuse.

Originally, polydrafters were required to conform to the polyiamond grid. Here I use extended polydrafters, which may depart from the polyiamond grid, as long as they obey the joining rules.

The strong surround number of a polydrafter is the fewest number of copies of the polydrafter that can surround it strongly; that is, surrounding even its corners. The drafter 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.

Here I show minimal known strong surrounds for the monodrafter and the didrafters. 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

  • Strong Surround Numbers for Polyaboloes
  • Strong Surround Numbers for Polycairos
  • Strong Surround Numbers for Polykites
  • Strong Surround Numbers for Polydoms
  • Monodrafter

    Didrafters

    There are 13 didrafters.

    Last revised 2026-06-08.


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    Col. George Sicherman [ HOME | MAIL ]