Strong Surround Numbers for Polykites

A polykite is a plane figure formed by kite-shaped sextants of cells in the Hex Grid. The strong surround number of a polykite is the fewest number of copies of the polykite that can surround it strongly; that is, including its corners. The polykite must conform to the hex grid.

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 strong surrounds for small polykites, the smallest polykites with given surround numbers, and the smallest polykite with no strong surrounds.

See also

  • Strong Surround Numbers for Polyaboloes
  • Strong Surround Numbers for Polycairos

    • Minimal Strong Surrounds

    An exclamation point (!) indicates that the solution is unique for the minimum number of tiles.

    Monokite

    Dikites

    Only one dikite can strongly surround itself.

    Trikites

    Tetrakites

    Minimal Polykites with Given Strong Surround Numbers

    3 Copies, 9 Cells

    Found by Juris Čerņenoks.

    4 Copies, 5 Cells

    5 Copies, 2 Cells

    6 Copies, 4 Cells

    7 Copies, 3 Cells

    8 Copies, 5 Cells

    9 Copies, 1 Cell

    10 Copies, 8 Cells

    11 Copies, 10 Cells

    12 Copies, 3 Cells

    Minimal Polykite that Cannot Surround Itself Strongly

    Last revised 2023-07-03.

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    Col. George Sicherman [ HOME | MAIL ]