Definition of self-avoiding-filling-polygon
In Euclidean graph where each vertex is a point on the $2D$ plane, so the weight of each edge is the Euclidean distance between the vertices. Self-avoiding-filling-polygon will be a path that visit each vertex exactly once and returning to the starting position without intersecting itself on the way.
How to calculate how many such polygons could be?
**Methods to create such polygons could be found here and here.*