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 Poly2ominoes. 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.


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Col. George Sicherman [ HOME | MAIL ]