Look up digon in Wiktionary, the free dictionary. 
In geometry, a digon is a degenerate polygon with two sides (edges) and two vertices.
A digon must be regular because its two edges are the same length. It has Schläfli symbol {2}.
In spherical tilings
In Euclidean geometry a digon is always degenerate. However, in spherical geometry a nondegenerate digon (with a nonzero interior area) can exist if the vertices are antipodal. The internal angle of the spherical digon vertex can be any angle between 0 and 180 degrees. Such a spherical polygon can also be called a lune.
One antipodal digon on the sphere.  Six antipodal digon faces on a hexagonal hosohedron tiling on the sphere. 
In polyhedra
A digon is considered degenerate face of a polyhedron because it has no geometric area and overlapping edges, but it can sometimes have a useful topological existence in transforming polyhedra.
Any polyhedron can be topologically modified by replacing an edge with a digon. Such an operation adds one edge and one face to the polyhedron, although the result is geometrically identical. This transformation has no effect on the Euler characteristic (χ=VE+F).
A digon face can also be created by geometrically collapsing a quadrilateral face by moving pairs of vertices to coincide in space. This digon can then be replaced by a single edge. It loses one face, two vertices, and three edges, again leaving the Euler characteristic unchanged.
Classes of polyhedra can be derived as degenerate forms of a primary polyhedron, with faces sometimes being degenerated into coinciding vertices. For example, this class of 7 uniform polyhedron with octahedral symmetry exist as degenerate forms of the great rhombicuboctahedron (4.6.8). This principle is used in the Wythoff construction.
4.4.4  3.8.8  3.4.3.4  4.6.6  3.3.3.3  3.4.4.4  4.6.8 
See also
 Dihedron  a degenerate polyhedron with 2 faces.
 Hosohedron  a degenerate polyhedron with 2 vertices.
 Demihypercube
References
 Weisstein, Eric W., "Digon" from MathWorld.
 A.B. Ivanov (2001), "Digon", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 9781556080104, http://www.encyclopediaofmath.org/index.php?title=D/d032390
External links

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