Convexification Numbers for Polyiamonds

Introduction

A polyiamond is a plane figure formed by joining equal equilateral triangles edge to edge.

In issue 14 of Rodolfo M. Kurchan's Puzzle Fun, Gustavo Piñeiro defines the rectification number of a polyomino as the least number of cells that can be left vacant when copies of the polyomino are packed in a rectangle.

Polyiamonds cannot form rectangles. Here I investigate the problem of packing copies of a polyiamond into some convex polyiamond, leaving as few cells as possible vacant.

In the results below, I omit polyiamonds that can tile some convex polyiamond without adding moniamonds. Such polyiamonds have Convexification Number 0.

Hexiamonds

4 Vacant Cells

Heptiamonds

1 Vacant Cell

2 Vacant Cells

3 Vacant Cells

4 Vacant Cells

6 Vacant Cells

Octiamonds

1 Vacant Cell

2 Vacant Cells

3 Vacant Cells

4 Vacant Cells

5 Vacant Cells

6 Vacant Cells

8 Vacant Cells

Enneiamonds

1 Vacant Cell

2 Vacant Cells

3 Vacant Cells

4 Vacant Cells

5 Vacant Cells

6 Vacant Cells

7 Vacant Cells

8 Vacant Cells

10 Vacant Cells

Last revised 2023-09-09.


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Col. George Sicherman [ HOME | MAIL ]