Abstract

The space of n-sided polygons embedded in three-space consists of a smooth manifold in which points correspond to piecewise linear or knots, while paths correspond to isotopies which preserve the geometric structure of these knots. Two cases are considered : (i) the space of polygons with varying edge length, and (ii) the space of equilateral polygons with unit -length edges. In each case, the spaces are explored via a Monte Carlo search to estimate the distinct knot types represented . Preliminary results of these searches are presented . Additionally, this data is analyzed to determine the smallest number of edges necessary to realize each knot type with nine or fewer crossings as a polygon , i.e. its minimal stick number.

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