|
In geometry, a polygon is degenerate if it either does not or cannot conform to the standard definitions in elementary geometry. For example in the Euclidean plane, any polygon which has fewer than three sides (edges) and fewer than three vertices will always be degenerate. Such figures need not be degenerate in all geometries, for example the ''digon'' is not degenerate when constructed between two antipodal points on a circle, or on as a spherical lune.〔Coxeter, ''Regular polytopes'', Chapter 1, ''Polygons and Polyhedra'', p.4 ''digon'', p.12 ''digon'' or ''lunes'', pp. 66-67 ''improper tessellations for p=2''.〕 The polygonal faces of some space-filling bubbles, such as the Williams β-tetrakaidecahedron, are degenerate because they are curved and cannot be flattened without destroying the space filling.〔Williams, R.; ''The Geometrical Foundation of Natural Structure'', Dover, 1978. ISBN 0-486-23729-X.〕 == Monogon == In geometry a monogon, also called henagon, or 1-gon, is a degenerate type of polygon with one edge and one vertex. It has Schläfli symbol 〔Coxeter, ''Introduction to geometry'', 1969, Second edition, sec 21.3 ''Regular maps'', p. 386-388〕 and can be constructed as an alternated digon, h. In Euclidean geometry a ''monogon'' with straight sides is an impossible object, because its endpoints must coincide, unlike any Euclidean line segment. For this reason, the ''monogon'' is not a proper polygon in Euclidean geometry. In the geometry of a circle, a ''monogon'' can be constructed as one vertex and a 360° arc edge with both ends sharing the same vertex. On a sphere a ''monogon'' can be constructed as a vertex on a great circle (equator). This forms a dihedron, , with two hemispherical ''monogonal'' faces which share one 360° edge and one vertex. Its dual is the hosohedron, , which has two antipodal vertices at the poles, one 360 degree lune face, and one edge (meridian) between the two vertices.〔 A truncated ''monogon'', t, is a digon, . |} 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Degenerate polygon」の詳細全文を読む スポンサード リンク
|