[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.
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