{{short description|Polygon with one edge and one vertex}} {{More citations needed|date=May 2026}} {{Infobox polygon | name = Monogon | image = Monogon.svg | caption = On a circle, a '''monogon''' is a tessellation with a single vertex, and one 360-degree arc edge. | type = Regular polygon | euler = | edges = 1 | schläfli = {1} or h{2} | wythoff = | coxeter = {{CDD|node}} or {{CDD|node_h|2x|node}} | symmetry = [ ], C<sub>s</sub> | area = | angle = | dual = Self-dual | properties = }} In geometry, a '''monogon''' is a curve, considered by some as a polygon with one edge and one vertex. It has Schläfli symbol {1}.<ref name=cox>Coxeter, ''Introduction to geometry'', 1969, Second edition, sec 21.3 ''Regular maps'', p. 386-388</ref>
==In Euclidean geometry== In Euclidean geometry a ''monogon'' is a degenerate polygon because its endpoints must coincide, unlike any Euclidean line segment. Most definitions of a polygon in Euclidean geometry do not admit the monogon.
==In spherical geometry== In spherical geometry, a monogon can be constructed as a vertex on a great circle (equator). This forms a dihedron, {1,2}, with two hemispherical monogonal faces which share one 360° edge and one vertex. Its dual, a hosohedron, {2,1} has two antipodal vertices at the poles, one 360° lune face, and one edge (meridian) between the two vertices.<ref name=cox />
{| class=wikitable |- align=center |160px<BR>Monogonal dihedron, {1,2} |160px<BR>Monogonal hosohedron, {2,1} |}
==See also== {{wiktionary|monogon}} * Digon
==References== {{reflist}} * Herbert Busemann, The geometry of geodesics. New York, Academic Press, 1955
{{clear}} {{polygons}} {{polyhedra}}
Category:Polygons by the number of sides Category:1 (number)