Can a nine gon be a tesselation?

Answer 1

I do not know the answer. However, I think that for a shape to be able to be a tesselation, that the exterior angle of it must be a factor of 360. The exterior angle of a 9-gon is 40 degrees, and since 40 x 9 is 360, then yes, the 9-gon will work in a tesselation (there will be four of them that share one vertex). In fact, I have come to this solution (it's probably been discovered before): All regular poylygons can be formed into a tesselation. The number of individual shapes in the tesselation that share each vertex will be equal to the number of sides on each polygon.