Vinsamlegast notið þetta auðkenni þegar þið vitnið til verksins eða tengið í það: http://hdl.handle.net/1946/26421
We extend the definition of regular star polygons and other regular star polygrams to be drawn within some non self-intersecting polygon instead of just regular polygons.
Instead of only connecting corners some constant apart, we allow any two corners of the polygon to be connected to form a figure.
These figures can be thought of as permutations consisting of some cycles where each cycle forms a polygon.
We define new permutation patterns called interacting cycle patterns that we use to describe properties of the permutations.
We describe some necessary properties for a permutation drawn within a polygon, such that its drawing forms a star.
Then we describe sufficient properties of permutations, such that when drawn within any available polygon they form stars.
Finally we describe sufficient properties of permutation drawings, that form a star in some polygon.