Polyming Irreptiling

Introduction

A polyming is a plane figure made by joining equal equilateral triangles in the polyiamond grid along edges and at corners. It is a generalization of polyiamonds, just as polykings are a generalization of polyominoes. A proper polyming is one that is not a polyiamond.

A reptiling is a dissection of a shape into smaller copies of itself, all the same size. An irreptiling is a dissection of a shape into smaller copies of itself, not necessarily of the same size. The term is due to Dr. Karl Scherer.

Here I show irreptilings of all proper polymings with 5 cells or less that use the fewest known tiles.

If you irreptile a polyming not shown, or by using fewer tiles than shown here, please write.

Many of these tilings first appeared in Erich Friedman's Math Magic for August 2010, which also shows irreptilings for polykings. For irreptilings of shapes other than polykings and polymings, see Math Magic for October 2002.