Polyomino Rectification with Holes

Introduction

Here I show minimal tilings of rectangles, allowing single-cell holes in the interior of the rectangle. The holes may not touch, even at corners.

I omit polyominoes with fewer than 5 cells. When minimal rectangles for such polyominoes exist, they have no holes.

Thanks to Jenard Cabilao for suggesting allowing holes when tiling rectangles.

For rectification without holes, see Mike Reid's Rectifiable Polyomino Page.

Pentominoes

1 Tile

2 Tiles

8 Tiles

10 Tiles

Hexominoes

1 Tile

2 Tiles

4 Tiles

10 Tiles

16 Tiles

49 Tiles

Heptominoes

1 Tile

2 Tiles

6 Tiles

8 Tiles

10 Tiles

12 Tiles

16 Tiles

20 Tiles

22 Tiles

24 Tiles

26 Tiles

36 Tiles

Octominoes

1 Tile

2 Tiles

4 Tiles

6 Tiles

10 Tiles

11 Tiles

12 Tiles

23 Tiles

24 Tiles

26 Tiles

30 Tiles

Enneominoes

1 Tile

2 Tiles

4 Tiles

8 Tiles

12 Tiles

20 Tiles

24 Tiles

25 Tiles

28 Tiles

Last revised 2023-09-17.