|Edges and vertices||2|
|Symmetry group||D2, , (*2•)|
In geometry, a digon, bigon, biangle or 2-gon is a polygon with two sides (edges) and two vertices. Its construction is degenerate in a Euclidean plane because the two sides would either coincide or one or both would have to be curved.
The digon is the simplest abstract polytope of rank 2.
In Euclidean geometry
A straight-sided digon is regular even though it is degenerate, because its two edges are the same length and its two angles are equal (both being zero degrees). As such, the regular digon is a constructible polygon.
Some definitions of a polygon do not consider the digon to be a proper polygon because of its degeneracy in the Euclidean case.
In elementary polyhedra
In spherical polyhedra
A spherical polyhedron can contain nondegenerate digons (with a nonzero interior area) if the vertices are antipodal. The internal angle of the spherical digon vertex can be any angle between 0 and 360 degrees. Such a spherical polygon can also be called a spherical lune.
One antipodal digon on the sphere.
Six antipodal digon faces on a hexagonal hosohedron tiling on the sphere.
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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.
- Coxeter, Regular polytopes, Chapter 1, Polygons and Polyhedra, p.4 digon, p.12 digon or lunes, pp. 66-67 improper tessellations for p=2. Cite error: Invalid
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- Herbert Busemann, The geometry of geodesics. New York, Academic Press, 1955
- Coxeter, Regular Polytopes (third edition). Dover Publications Inc. ISBN 0-486-61480-8
- Weisstein, Eric W., "Digon", MathWorld.
- A.B. Ivanov (2001), "Digon", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4
|Look up digon in Wiktionary, the free dictionary.|
- Media related to Digons at Wikimedia Commons