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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 ...
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 geometry, a star polyhedron is a polyhedron which has some repetitive quality of nonconvexity giving it a star-like visual quality. There are two general kinds of star polyhedron: Polyhedra which self-intersect in a repetitive way. Concave polyhedra of a particular kind which alternate convex and concave or saddle vertices in a repetitive way.
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 ...
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 ...
A convex regular polygon having n sides is denoted by {n}. So an equilateral triangle is {3}, a square {4}, and so on indefinitely. A regular n-sided star polygon which winds m times around its centre is denoted by the fractional value {n/m}, where n and m are co-prime, so a regular pentagram is {5/2}.
In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called a lateral face. A pyramid is a conic solid with a polygonal base. Many types of pyramids can be found by determining the shape of bases, either by based on a regular polygon (regular pyramids ...
A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags. A regular polyhedron is highly symmetrical, being all of edge-transitive, vertex-transitive and face-transitive. In classical contexts, many different equivalent definitions are used; a common one is that the faces are congruent regular polygons which are ...