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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 ...
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. They use the same vertices as the convex forms, but connect in an alternate connectivity which passes around the circle more than once to be completed.
A non-convex regular polygon is a regular star polygon. The most common example is the pentagram, which has the same vertices as a pentagon, but connects alternating vertices. For an n-sided star polygon, the Schläfli symbol is modified to indicate the density or "starriness" m of the polygon, as {n/m}.
In mathematics, a regular 4-polytope or regular polychoron is a regular four-dimensional polytope. They are the four-dimensional analogues of the regular polyhedra in three dimensions and the regular polygons in two dimensions. There are six convex and ten star regular 4-polytopes, giving a total of sixteen.
Convex polygon; Concave polygon; Constructible polygon; Cyclic polygon; ... (Regular star 4-polytope) Icosahedral 120-cell, Small stellated 120-cell, Great 120-cell, ...
Regular convex and star polygons with 3 to 12 vertices labelled with their Schläfli symbols. Stellating a regular polygon symmetrically creates a regular star polygon or polygonal compound. These polygons are characterised by the number of times m that the polygonal boundary winds around the centre of the figure. Like all regular polygons ...
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 ...
The uniform and dual uniform star polyhedra are also self-intersecting polyhedra. They may either have self-intersecting faces, or self-intersecting vertex figures or both. The uniform star polyhedra have regular faces or regular star polygon faces. The dual uniform star polyhedra have regular faces or regular star polygon vertex figures.