# 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.

See also Tiling an L Shape with
the 12 Pentominoes.

- General Solutions
- Diagonal Symmetry

## General Solutions

Polyominoes not shown have no known solution.
The largest hexomino and octomino solutions
are formed by joining two rectangular tilings.
They are 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.

*Last revised 2023-09-10.*

Back to Polyomino and Polyking Tiling
< Polyform Tiling
<
Polyform Curiosities

Col. George Sicherman
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