A [[sequence]] of [[Point|points]] called [[vertex|vertices]] along with the [[Line, Line-Segment, Ray|line-segments]] that connect consecutive vertices. - simple polygonal chains contain intersections only at end points between consecutive segments - self-intersecting (non-simple) polygonal chains have intersections between non-consecutive segments - closed polygonal chains contain an additional segment between their first and last vertices - monotone polygonal chains are ones for which there exist a line which has normals that intersect the chain only once (think functions and vertical line test) - conjecture: monotone polygonal chains do not contain a signed (consecutive) series of angles that exceed a magnitude of $180^\circ$