the digon to be a proper polygon because of its degeneracy in the Euclidean case. In elementary polyhedra A digon as a face of a polyhedron is degenerate because it is a degenerate polygon. But sometimes it can have a useful topological existence in transforming polyhedra. As a spherical lune A spherical lune is a digon whose two vertices are antipodal points on the sphere. A spherical polyhedron constructed from such digons is called a hosohedron. Theoretical significance The digon is an important construct in the topological theory of networks such as graphs and polyhedral surfaces. Topological equivalences may be established using a process of reduction to a minimal set of polygons, without affecting the global topological characteristics such as the Euler value. The digon represents a stage in the simplification where it can be simply removed and substituted by a line segment, without affecting the overall characteristics. The cyclic groups may be obtained as rotation symmetries of polygons: the rotational symmetries of the digon provide the group C2. See also Monogon Demihypercube References Citations Bibliography Herbert Busemann, The geometry of geodesics. New York, Academic Press, 1955 Coxeter, Regular Polytopes (third edition), Dover Publications Inc, 1973 External links Polygons by the number of sides 2 (number)