Holey Polyiamond Hexagon Tilings

Which polyiamonds can tile regular hexagons, allowing isolated one-cell holes? Here are the smallest regular hexagons that can be tiled by a given polyiamond with one-cell holes that do not touch the perimeter or one another. The tilings shown are not necessarily unique.

If you find a smaller solution or solve an unsolved case, please write.

  • Tetriamonds
  • Pentiamonds
  • Hexiamonds
  • Heptiamonds
  • Octiamonds
  • Tetriamonds

    Pentiamonds

    Impossible

    Hexiamonds

    Impossible

    Heptiamonds

    Unsolved

    Holes on the Perimeter

    These heptiamonds have solutions if we let holes touch the perimeter.

    Octiamonds

    Holes on the Perimeter

    These octiamonds have solutions if we let holes touch the perimeter.

    Last revised 2025-12-25.


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    Col. George Sicherman [ HOME | MAIL ]