Polyiamond Convexification with Holes

Introduction

A polyiamond is a figure made by joining equal equilateral triangles edge to edge. Some polyiamonds can tile convex shapes. Most cannot.

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

I omit polyiamonds with fewer than 4 cells. They are already convex.

For convexity without holes, see Minimal Convex Polyiamond Tilings.

Tetriamonds

1 Tile

3 Tiles

Pentiamonds

1 Tile

2 Tiles

3 Tiles

Hexiamonds

1 Tile

2 Tiles

4 Tiles

8 Tiles

9 Tiles

Heptiamonds

1 Tile

2 Tiles

3 Tiles

4 Tiles

12 Tiles

14 Tiles

Octiamonds

1 Tile

2 Tiles

4 Tiles

6 Tiles

8 Tiles

18 Tiles

Enneiamonds

1 Tile

2 Tiles

4 Tiles

6 Tiles

12 Tiles

18 Tiles

Dekiamonds

1 Tile

2 Tiles

3 Tiles

4 Tiles

8 Tiles

9 Tiles

12 Tiles

21 Tiles

Last revised 2023-09-17.

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Col. George Sicherman [ HOME | MAIL ]