# DIMACS Discrete Mathematics Seminar

## Title:

Regular Zig-zag Polygons in the Plane

## Speaker:

- Robert Jamsion
- Clemson University

## Place:

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

## Time:

- 4:30 PM
- Tuesday, May 9, 1995

## Abstract:

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