Digon

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Digon
Rank2
TypeRegular
SpaceSpherical
Notation
Coxeter diagramx2o ()
Schläfli symbol{2}
Elements
Edges2
Vertices2
Vertex figureDyad, length 0
Measures (edge length 1)
Angle
Central density1
Related polytopes
ArmyDigon
DualDigon
ConjugateNone
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryK2, order 4
ConvexYes

A digon is a polygon with two sides. It is degenerate if embedded in Euclidean space, as its edges coincide. It can however be thought of as a tiling of the circle. In two-dimensional or higher spherical space, it can form a lune such as the ones making up a hosohedron.

In Euclidean space, a convex n -gon can be formed as the intersection of n  half-planes, so one possible realization of a Euclidean digon is as the intersection of two parallel half-planes, forming an infinite "stripe" with two ideal vertices.

It is the only rank 2 ditope and hosotope. It is also the two-dimensional demihypercube.

The digon is the only non-lattice polygon and the simplest non-lattice polytope. In turn, many (though not all) non-lattice polytopes contain digonal sections.

The digon is the simplest possible polygon, as monogons are disallowed under almost all definitions of a polytope. Despite this, it may be built as the omnitruncate of a (generalized) complex with two flags and two flag-changes between them. As such, this complex is called the monogonal complex.

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