Edgeface

Edgeface is a term encountered in geometry and computer graphics to describe the relationship between an edge and the faces that share that edge on a polyhedral surface or mesh. It is not standardized as a formal mathematical object, but is used to refer to the set of incidences involving a given edge and its adjacent faces.

In convex polyhedra, every edge lies on exactly two faces; those faces are adjacent along the edge. The collection of edge-face incidences can be represented by incidence structures such as the edge-face graph, where nodes represent edges and faces and connections indicate which faces meet along which edges.

In mesh processing and rendering, knowledge of edge-face relationships is essential for traversal, normal calculation, and topological integrity checks. Algorithms for subdivision, simplification, or smoothing typically rely on knowing which faces share an edge and which edges bound a face.

Other uses of the term edgeface may appear as a product name, project label, or informal shorthand in different fields. Because the term is not part of a single standard vocabulary, authors should define it clearly when it is used. See also polyhedron, edge, face, incidence relation, Euler's formula.