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  2. Star polygon - Wikipedia

    en.wikipedia.org/wiki/Star_polygon

    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 ...

  3. Regular polygon - Wikipedia

    en.wikipedia.org/wiki/Regular_polygon

    For an n-sided star polygon, the Schläfli symbol is modified to indicate the density or "starriness" m of the polygon, as {n/m}. If m is 2, for example, then every second point is joined. If m is 3, then every third point is joined. The boundary of the polygon winds around the center m times. The (non-degenerate) regular stars of up to 12 ...

  4. Stellation - Wikipedia

    en.wikipedia.org/wiki/Stellation

    The case m = 1 gives the convex polygon {n}. m also must be less than half of n; otherwise the lines will either be parallel or diverge, preventing the figure from ever closing. If n and m do have a common factor, then the figure is a regular compound. For example {6/2} is the regular compound of two triangles {3} or hexagram, while {10/4} is a ...

  5. Antiprism - Wikipedia

    en.wikipedia.org/wiki/Antiprism

    Example: a retrograde star antiprism with regular star 7/5-gon bases (vertex configuration: 3.3.3.7/5) cannot be uniform. Also, star antiprism compounds with regular star p/q-gon bases can be constructed if p and q have common factors. Example: a star 10/4-antiprism is the compound of two star 5/2-antiprisms.

  6. Regular polyhedron - Wikipedia

    en.wikipedia.org/wiki/Regular_polyhedron

    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 ...

  7. Regular polytope - Wikipedia

    en.wikipedia.org/wiki/Regular_polytope

    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}.

  8. List of regular polytope compounds - Wikipedia

    en.wikipedia.org/wiki/List_of_regular_polytope...

    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 ...

  9. Star polyhedron - Wikipedia

    en.wikipedia.org/wiki/Star_polyhedron

    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.