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In geometry, a star-shaped polygon is a polygonal region in the plane that is a star domain, that is, a polygon that contains a point from which the entire polygon boundary is visible. Formally, a polygon P is star-shaped if there exists a point z such that for each point p of P the segment z p ¯ {\displaystyle {\overline {zp}}} lies ...
Regular convex and star polygons with 3 to 12 vertices, labeled with their Schläfli symbols A regular star polygon is a self-intersecting, equilateral, and equiangular polygon . A regular star polygon is denoted by its Schläfli symbol { p / q }, where p (the number of vertices) and q (the density ) are relatively prime (they share no factors ...
The polytopes of rank 2 (2-polytopes) are called polygons.Regular polygons are equilateral and cyclic.A p-gonal regular polygon is represented by Schläfli symbol {p}.. Many sources only consider convex polygons, but star polygons, like the pentagram, when considered, can also be regular.
The convex forms are listed in order of degree of vertex configurations from 3 faces/vertex and up, and in increasing sides per face. This ordering allows topological similarities to be shown. There are infinitely many prisms and antiprisms, one for each regular polygon; the ones up to the 12-gonal cases are listed.
∞ star polygons: 1: 1: 0: 0: ... Convex polygon; Concave polygon; ... This is a table of all the shapes above. Table of Shapes Section Sub-Section
The intersection of two convex polygons is a convex polygon. A convex polygon may be triangulated in linear time through a fan triangulation, consisting in adding diagonals from one vertex to all other vertices. Helly's theorem: For every collection of at least three convex polygons: if all intersections of all but one polygon are nonempty ...
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