An equilateral polygon has sides of equal length, an equiangular polygon has equal angles. Only for a triangle the equilateral and equiangular version gives the same figure. The two qualities together make a regular polygon. The more sides the polygon has, the more it approximates a circle. The genius mathematician Gauss showed - in the age of 18 - which regular polygons can be constructed with a pair of compasses and a ruler 2). For example the regular heptadecagon has this quality.
The polygons have been given own names, derived from the Greek numerals:
The first two polygons mentioned are one-dimensional, they consist both of just one side.
Some polygons derive their qualities in relation to their position according another curve:
A so-called control polygon is used to define a curve by points near the curve, not by points on the curve.
In the field of Roman ancient history the so called Thijssen polygons are in use: these polygons have been constructed around Roman district capitals, to approximate the districts' boundaries.
1) Poly (Gr.) = many, goonia (Gr.) = angle.
2) When n is the number of sides, then for be able to construct by a pair of compasses, n has to obey: