tessellations for a pot?

[MJ25]

I've done lang's pots from the crease patterns on his page a couple of times, and I was thinking if you did it with some tessellation it'd look amazing, does any of you know how I could make a tessellation on a 15 16 or 17 sided regular polygon, making it be regular when you're finished, or to get that out of a square?

[Jonnycakes]

Well, I think there are constructions to get 15, 16, and 17-gons from a square, but they will not regularly tile. You could devise a method to get them in a regular pattern, but there will be gaps in-between them.