DIMACS Discrete Mathematics Seminar


Regular Zig-zag Polygons in the Plane


Robert Jamsion
Clemson University


DIMACS Seminar Room, CoRE Building, Room 431
Busch Campus, Rutgers University


4:30 PM
Tuesday, May 9, 1995


A plane polygon is regular if all of its sides have the same length and all of its angles are equal. If we relax, the equiangular condition by allowing the angles at different vertices to possibly differ in sense but not in magnitude, a very rich class of polygonal structures arises. These pararegular polygons were first suggested by the study of configuration spaces of certain bar and joint frameworks. These frameworks represent possible molecular configurations where certain interatomic distances are fixed. Usually such frameworks are 3-dimensional. When they collapse into the plane, the result is a singularity in the configuration space. One of the first questions is whether pararegular polygons exist with angles other than those occuring in the regular polygons. The answer is YES and we can give a complete description of the possible angles as well as an algorithm for building all pararegular polygons on a given number of sides.
Document last modified on May 4, 1995