# Polyiamond Convexification with Holes

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.

### 1 Tile

### 3 Tiles

### 1 Tile

### 2 Tiles

### 3 Tiles

### 1 Tile

### 2 Tiles

### 4 Tiles

### 8 Tiles

### 9 Tiles

### 1 Tile

### 2 Tiles

### 3 Tiles

### 4 Tiles

### 12 Tiles

### 14 Tiles

### 1 Tile

### 2 Tiles

### 4 Tiles

### 6 Tiles

### 8 Tiles

### 18 Tiles

### 1 Tile

### 2 Tiles

### 4 Tiles

### 6 Tiles

### 12 Tiles

### 18 Tiles

### 1 Tile

### 2 Tiles

### 3 Tiles

### 4 Tiles

### 8 Tiles

### 9 Tiles

### 12 Tiles

### 21 Tiles

Last revised 2023-09-17.

Back to Polyiamond and Polyming Tiling
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Polyform Curiosities

Col. George Sicherman
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