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.
Back to Polyiamond and Polyming Tiling
< Polyform Tiling
< Polyform Curiosities
Col. George Sicherman
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