It is well-known that the only regular polygons which tessellate the plane (using only one shape) are the triangle, square, and hexagon. However, there are many more tessellations of the plane by polygons which are irregular.
However, the triangle and square may be tessellated into larger versions of themselves, making a larger triangle or larger square, respectively. The hexagon does not have this property, as one cannot form a larger regular hexagon from smaller regular hexagons.
Are there any irregular polygons (besides the triangle and rectangle) which can perfectly tessellate larger versions of themselves?
I have attempted to create examples of my own, but have come to the conclusion there probably are none. I conjecture that having more than four sides forces tessellations to be non-convex, but have not been able to prove that. Would anybody have ideas for a proof that there are none, or contrarily an example of one?
Thanks to Blue's judicious comment, I have found the word for this and a source to look at some examples! See https://en.wikipedia.org/wiki/Rep-tile.