Journal of Theoretical Physics & Mathematics Research

Symmetries of p-Polygons

Abstract

Rolf Haag

In addition to general considerations, the present work includes the enumeration of the equivalence-classes of p-polygons with p vertices for p ≥ 5 with certain symmetry properties:

1. We count the equivalence-classes of p-polygons with p symmetry axes, the so-called regular polygons.
2. We count the equivalence-classes of p-polygons with exactly one axis of symmetry.
3. We count the equivalence-classes of p-polygons with no axis of symmetry, the so-called asymmetrical p-polygons.

For p = 5 and p = 7 we show in all three cases a set of representatifs of the equivalence classes.

PDF