Sidedifferent

Sidedifferent is a roughly informal mathematical term used to describe a polygon in which no two sides have the same length. It is not standard terminology, and many texts refer to the same idea via scalene or irregular polygons. In triangles, a sidedifferent triangle is what most would call a scalene triangle: all three side lengths are different. For polygons with four or more sides, a polygon with pairwise unequal side lengths is sometimes called a sidedifferent polygon, though the more common label is simply a scalene polygon, or an irregular polygon when angle measures vary.

The main characteristic is the absence of equal-length sides. This generally implies minimal or no symmetry; in practice a sidedifferent n-gon has only the trivial symmetry (the identity) unless other geometric coincidences occur.

Construction and existence: To form a simple polygon with specified distinct side lengths, a necessary condition is that the longest side be shorter than the sum of the remaining sides (polygon inequality). Beyond this, arranging the sides and angles to close the figure requires appropriate turning angles, which is always possible in many cases.

Relationship to symmetry and angles: No requirement on interior angles; some may be acute, obtuse, or right, as long as all sides differ. The property concerns side lengths, not angle measures.

See also: Scalene polygon; Irregular polygon.