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Individual polygons are named (and sometimes classified) according to the number of sides, combining a Greek-derived numerical prefix with the suffix -gon, e.g. pentagon, dodecagon. The triangle, quadrilateral and nonagon are exceptions, although the regular forms trigon, tetragon, and enneagon are sometimes encountered as well.
A polytope is a geometric object with flat sides, which exists in any general number of dimensions. The following list of polygons, polyhedra and polytopes gives the names of various classes of polytopes and lists some specific examples.
Spherical polygons play an important role in cartography (map making) and in Wythoff's construction of the uniform polyhedra. A skew polygon does not lie in a flat plane, but zigzags in three (or more) dimensions. The Petrie polygons of the regular polytopes are well known examples.
Star polygon – there are multiple types of stars Pentagram - star polygon with 5 sides; Hexagram – star polygon with 6 sides Star of David (example) Heptagram – star polygon with 7 sides; Octagram – star polygon with 8 sides Star of Lakshmi (example) Enneagram - star polygon with 9 sides; Decagram - star polygon with 10 sides
List of polygons, polyhedra and polytopes. List of regular polytopes and compounds; Elsewhere. Solid geometry, including table of major three-dimensional shapes;
More generally regular skew polygons can be defined in n-space. Examples include the Petrie polygons, polygonal paths of edges that divide a regular polytope into two halves, and seen as a regular polygon in orthogonal projection. In the infinite limit regular skew polygons become skew apeirogons.
Simple polygons are sometimes called Jordan polygons, because they are Jordan curves; the Jordan curve theorem can be used to prove that such a polygon divides the plane into two regions. [8] Indeed, Camille Jordan 's original proof of this theorem took the special case of simple polygons (stated without proof) as its starting point. [ 9 ]
In geometry, a bigon, [1] digon, or a 2-gon, is a polygon with two sides and two vertices.Its construction is degenerate in a Euclidean plane because either the two sides would coincide or one or both would have to be curved; however, it can be easily visualised in elliptic space.