Sidemes

Sidemes is a term that appears in a small number of mathematical and interdisciplinary discussions but does not have a single, widely accepted definition. The word is encountered as a neologism describing geometric constructs tied to the sides of polygons, and its precise meaning varies by author.

In geometry, sideme is sometimes used to denote a line segment associated with a side of a polygon. A common informal usage describes sidemes as the segments that connect a polygon vertex to the midpoint of an opposite side, a generalization of the triangle median. In this sense, sidemes inherit properties reminiscent of medians, such as symmetry in regular polygons and potential relationships to area. However, because not all polygons have a clearly defined opposite side for every vertex, this usage is limited to certain polygon classes or described only in exploratory or expository texts.

In other contexts, sidemes may refer to collections of side midpoints themselves or to networks formed by joining consecutive side midpoints, akin to a medial polygon. Some authors use the term metaphorically to discuss side-based substructures in graph drawings or mesh generation.

Because the term is not standardized, readers should consult the original sources for a given sideme definition. See also medians, medial polygon, polygon geometry, and side.