Tiling an L Shape with a Polyomino

Introduction

The problem of arranging copies of a polyomino to form a rectangle has received much attention. The corresponding problem for an L shape has not.

In general, it is easier to tile rectangles than L shapes, because rectangles can often be tiled with rotary symmetry. However, for some polyominoes the minimal rectangles cannot be tiled symmetrically.

Here I show the smallest known L shapes, measured by area, that can be tiled with given polyominoes. If you find a smaller solution or solve an unsolved case, please write. In particular, the largest known hexomino and octomino solutions are formed by joining two rectangle tilings. They are not likely to be minimal.

See also Tiling an L Shape with the 12 Pentominoes.

Solutions

Polyominoes not shown have no known solution.

Monomino

Domino

Trominoes

Tetrominoes

Pentominoes

Hexominoes

Heptominoes

Octominoes

Last revised 2022-11-16.


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Col. George Sicherman [ HOME | MAIL ]