With any polysquare or polyiamond you can ask whether such a shape tiles a square or triangle in an irregular way (i.e., using copies of various sizes). For this Demonstration the most interesting cases of irregular tilings have been selected.
Since the author's book was published on irreptiles, the problem area of irregular tilings has seen a steadily growing interest amongst puzzlists.
Many very simple cases of irregular tilings and quite a few complicated cases are omitted in this Demonstration. Also excluded are all self-tilings of irreptiles; they are covered by the separate Demonstration "Irreptiles", created by the same author.
Diagrams 1-17: Irregular tilings of the regular triangle.
Diagrams 18-26: Irregular tilings of the isosceles right triangle.
Diagrams 27-36: Irregular tilings of the square.
Diagram 37: Irregular tiling of the regular hexagon.
Diagrams 38, 39: Overviews of the shapes presented in this Demonstration.
A shape which irregularly tiles a rectangle is called irrectifiable.
A shape which irregularly tiles itself is called an irreptile.
A shape which regularly tiles itself is called a rep-tile.
Contributions by other authors:
Rodolpho Kurchan: diagrams 10 and 32
Michael Reid: diagrams 23, 29
Tetsu Kawahara: diagram 30
Browse all topics
