Digon
| Digon | |
|---|---|
 | |
| Rank | 2 |
| Type | Regular |
| Space | Spherical |
| Notation | |
| Coxeter diagram | x2o |
| Schläfli symbol | {2} |
| Elements | |
| Edges | 2 |
| Vertices | 2 |
| Vertex figure | Dyad, length 0 |
| Measures (edge length 1) | |
| Angle | 0° |
| Central density | 1 |
| Related polytopes | |
| Army | Digon |
| Dual | Digon |
| Conjugate | None |
| Abstract & topological properties | |
| Euler characteristic | 0 |
| Orientable | Yes |
| Properties | |
| Symmetry | K2, order 4 |
| Convex | Yes |
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 two-dimensional 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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