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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) and where q ≥ 2. The density of a polygon can also be called its turning number: the sum of ...
Stellation. Construction of a stellated dodecagon: a regular polygon with Schläfli symbol {12/5}. In geometry, stellation is the process of extending a polygon in two dimensions, a polyhedron in three dimensions, or, in general, a polytope in n dimensions to form a new figure. Starting with an original figure, the process extends specific ...
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 }.
Polygon. Some polygons of different kinds: open (excluding its boundary), boundary only (excluding interior), closed (including both boundary and interior), and self-intersecting. In geometry, a polygon (/ ˈpɒlɪɡɒn /) is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal ...
A regular enneagram is a 9-sided star polygon. It is constructed using the same points as the regular enneagon, but the points are connected in fixed steps. Two forms of regular enneagram exist: One form connects every second point and is represented by the Schläfli symbol {9/2}.
For any natural number n, there are n-pointed star regular polygonal stars with Schläfli symbols {n/m} for all m such that m < n/2 (strictly speaking {n/m}= {n/ (n−m)}) and m and n are coprime. When m and n are not coprime, the star polygon obtained will be a regular polygon with n / m sides. A new figure is obtained by rotating these ...
In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry.In particular, all its elements or j-faces (for all 0 ≤ j ≤ n, where n is the dimension of the polytope) — cells, faces and so on — are also transitive on the symmetries of the polytope, and are themselves regular polytopes of dimension j≤ n.
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.