[seqfan] Self-intersecting n-gons

David Wilson davidwwilson at comcast.net
Tue May 15 02:45:07 CEST 2018

How many distinct n-gons are there in the plane, if

- edges are straight line segments connected cyclically at vertices (as in a
regular n-gon).
- No vertex may lie on another vertex or interior point of an edge.
- Two edges may intersect at a point interior to each edge, but three or
more edges may not intersect at the same point.

 Two n-gons are equivalent if the vertices of one may be moved continuously
to the vertices of the other without violating the above rules at any point.

For n >= 3, let a(n) be the number of non-equivalent n-gons.

a(3) = 1, the triangle.
a(4) = 2, the standard and crossed quadrilaterals.
a(5) >= 5.

I suspect the sequence grows superexponentially.

More information about the SeqFan mailing list