# Multiple Compatibility for Polyominoes

## Introduction

A set of polyforms is *compatible*
if there exists a figure that each of them can tile.
Here are minimal figures that can be tiled by a given number of
*n*-ominoes.
Most are taken from Jorge Luis Mireles's defunct site
**Poly**^{2}ominoes.
If you find a smaller solution or one that can be tiled by more
*n*-ominoes, please write.
For arbitrary sets of three pentominoes, see Livio Zucca's
Triple Pentominoes.
For arbitrary sets of four pentominoes, see
Quadruple Pentominoes.

For other polyforms,
see Multiple Compatibility
for Polyiamonds,
Multiple Compatibility
for Polyhexes,
and
Multiple Compatibility
for Polypents.

## Trominoes

### 2 Trominoes

## Tetrominoes

### 3 Tetrominoes

### 4 Tetrominoes

### 5 Tetrominoes

## Pentominoes

### 4 Pentominoes

### 5 Pentominoes

#### Solutions Using Other Pentominoes

##### 5T, 5X

##### 5V, 5W

##### 5N

##### 5U

##### 5I

### 6 Pentominoes

*Rodolfo Kurchan*
#### Solutions Using Other Pentominoes

##### 5N, 5U, 5W

##### 5I

##### 5X

##### 5Z

### 7 Pentominoes

#### Alternate Solution

#### Holeless Solution

#### Historic Solution

This was the first solution found:

*Mike Reid*

### 8 Pentominoes

## Hexominoes

### 6 Hexominoes

#### Solutions Using Other Hexominoes

### 9 Hexominoes

#### Solutions Using Other Hexominoes

### 10 Hexominoes

*Mike Reid*
### 11 Hexominoes

*Mike Reid*
### 12 Hexominoes

*Mike Reid*
## Heptominoes

### 9 Heptominoes

### 14 Heptominoes

*Robert Reid*
### 15 Heptominoes

Last revised 2014-08-30.

Back to Multiple Compatibility
< Polyform Compatibility
< Polyform Curiosities

Col. George Sicherman
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