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.

General Solutions
Diagonal Symmetry

General Solutions

Polyominoes not shown have no known solution.

The largest octomino solution is formed by joining two rectangular tilings. It is not likely to be minimal.

One-Sided Variant

Diagonal Symmetry

Polyominoes not shown have no known solution.

The largest hexomino, heptomino, and octomino solutions are formed by joining two rectangular tilings. They may not be the smallest possible solutions.