Tiling a Triangle with Scaled Polymings

A polyming is a plane figure formed by joining cells in the equilateral triangle grid at edges or corners. I except polymings that are also polyiamonds; that is, polymings whose cells are all joined at edges.

Here I show known tilings of a triangle by scaled polymings that use the fewest tiles. If you find a solution with fewer tiles, or solve an unsolved polyming, please write.

Thanks to Rik Smoody for suggesting an improvement in the text of this page.

Dimings

Trimings

Tetramings

Pentamings

The only scaled proper pentaming known to tile a triangle is this one:

With 8 scaled copies of this pentaming, a straight tetriamond can be formed:

With 1 copy of this tetriamond and 10 copies of the pentaming, a V tetriamond can be formed:

With 8 scaled copies of the pentaming, a straight hexiamond can be formed:

With one copy of each of these 3 shapes and 15 copies of the pentaming, a triangle can be formed:

Hexamings

Last revised 2024-06-13.

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Col. George Sicherman [ HOME | MAIL ]