Polydom Irreptiling

Introduction

A reptiling of a polyform is a dissection of it into two or more equal pieces similar to the original polyform. An irreptiling of a polyform is a dissection of it into pieces similar to the original polyform, but not necessarily of equal size. Some shapes have irreptilings and no reptilings.

For irreptilings of polyforms other than polydoms, see Erich Friedman's Math Magic for October 2002. For more information about irreptiles, see Dr. Karl Scherer's book A Puzzling Journey to the Reptiles and Related Animals.

Here I omit polydoms that are similar to polydoms with fewer cells, and I show only solutions with the fewest possible pieces. Irreptilings that are reptilings appear in green. Polydoms that are also polyominoes appear with gray backgrounds. If you find a solution with fewer pieces, or solve an unsolved case, please write.

Monodom

2

Didoms

4
4
4
4
4

Tridoms

8
	Karl Scherer
6
9

Tetradoms

	Karl Scherer
9
4
4
4
	Bryce Herdt
15
4
4
4
4
4
	Bryce Herdt
14

Pentadoms

6
6
17
16

Hexadoms

4
9
10
4
6
6
6
6
4
4
4
6
6
18
13
9
4
4
13

Heptadoms

19
13
6
8

Octadoms

4
9
21
	Karl Scherer
8
4
4
4
8

Last revised 2023-08-13.