Tiling the plane with one of each $n$-gon

Inspired by a question on MathOverflow.

Can you tile the plane with one of each $n$-gon?

Yes: put the vertices on concentric circles. Start with a triangle in the middle. Then, for each layer, use two points on the inner layer, two points at the same angle on the next layer, and any more points between those. Work round each layer until you run out of points, then start a new layer.