An irreptile is a geometric shape that can be divided into smaller pieces, not necessarily equal, with the same shape as the original.
The term irreptile was coined by Dr. Karl Scherer, who studied such tilings extensively. His results appear in chapters 3 and 4 of his book A Puzzling Journey to the Reptiles and Related Animals, and in some of his Wolfram Demonstrations, notably Irreptiles and Some Irreptiles of Order Greater Than 20.
Erich Friedman's Math Magic for October 2010 presents irreptilings for polykings and polymings, which are also vertex-connected polyforms.
Here I present minimal known irreptilings for proper polyfetts—those that are not also polyaboloes. Polyfetts with the same shapes as smaller polyfetts are omitted. Proper reptilings are shown in shades of blue.
See also Polyabolo Irreptiles.
Last revised 2020-09-26.