Spirolateral

Spirolaterals are a class of polygons, mostly self-intersecting, that generally have a single internal angle and a sequence of edge lengths formed from repetitions of the sequence 1, 2, ..., n.

A simple spirolateral is constructed as follows: draw a 1-unit line segment, turn &phi; degrees clockwise, draw a 2-unit line segment, turn &phi; degrees clockwise, ... draw an n-unit line segment, turn &phi; degrees clockwise, repeat from the beginning. The process is immediately halted when one returns to the original point, forming a closed polygon that is usually self-intersecting. Defining &theta; = 180° - &phi; as the internal angle, every simple spirolateral is uniquely identified by n and &theta;, and notated as n&theta;.