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Regular digon
On a circle, a digon is a tessellation with two antipodal points, and two 180° arc edges.
Type Regular polygon
Edges and vertices 2
Schläfli symbol {2}
Coxeter diagram CDel node 1.pngCDel 2x.pngCDel node.png
Symmetry group D2, [2], (*2•)
Dual polygon Self-dual

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.

A regular digon is represented by Schläfli symbol {2} and may be constructed on a sphere as a pair of 180 degree arcs connecting antipodal points, when it forms a lune.[1]

The digon is the simplest abstract polytope of rank 2.

In Euclidean geometry[edit]

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.[2]

Some definitions of a polygon do not consider the digon to be a proper polygon because of its degeneracy in the Euclidean case.[1]

In elementary polyhedra[edit]

A nonequilateral truncated cuboctahedron has blue rectangular faces that degenerate into digons in the cubic limit.

A digon is considered a degenerate face of a polyhedron because it has no geometric area and its edges coincide. But sometimes it can have a useful topological existence in transforming polyhedra.

In spherical polyhedra[edit]

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.

A truncated digon, t{2} is a square, {4}. An alternated digon, h{2} is a monogon, {1}.

Theoretical significance[edit]

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.

See also[edit]


  1. ^ a b 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 <ref> tag; name "cox2" defined multiple times with different content (see the help page).
  2. ^ http://www.math.iastate.edu/thesisarchive/MSM/EekhoffMSMSS07.pdf

External links[edit]

  • Media related to Digons at Wikimedia Commons