Tiling a Rectangle with a Scaled Polyomino

Introduction

A polyomino is a figure made by joining equal squares edge to edge. Some polyominoes can tile rectangles. Most cannot.

A scaled polyomino is a polyomino that may be enlarged by various integer scale factors. That is, it is a family of similar polyominoes.

Here I show minimal tilings of rectangles by various scaled polyominoes. Polyominoes that are rectangles are shown in violet. Polyominoes whose minimal scaled tiling of a rectangle is the same as a minimal tiling without scaling appear in green, with a link to such a minimal tiling at Michael Reid's Rectifiable Polyomino Page.

For all other minimal scaled tilings, the number of tiles in the minimal non-scaled rectangle tiling appears in parentheses after the number of tiles in the minimal scaled tiling.

Scaled polyominoes for which no known rectangle tiling is known do not appear below. If you find such a tiling, or find a solution with fewer tiles than the solution shown below, please write.

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Col. George Sicherman [ HOME | MAIL ]