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  2. Star-shaped polygon - Wikipedia

    en.wikipedia.org/wiki/Star-shaped_polygon

    If a star-shaped polygon is convex, the link distance between any two of its points (the minimum number of sequential line segments sufficient to connect those points) is 1, and so the polygon's link diameter (the maximum link distance over all pairs of points) is 1. If a star-shaped polygon is not convex, the link distance between a point in ...

  3. Star polygon - Wikipedia

    en.wikipedia.org/wiki/Star_polygon

    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 ...

  4. List of uniform polyhedra - Wikipedia

    en.wikipedia.org/wiki/List_of_uniform_polyhedra

    Uniform polyhedra can be divided between convex forms with convex regular polygon faces and star forms. Star forms have either regular star polygon faces or vertex figures or both. This list includes these: all 75 nonprismatic uniform polyhedra; a few representatives of the infinite sets of prisms and antiprisms;

  5. List of regular polytopes - Wikipedia

    en.wikipedia.org/wiki/List_of_regular_polytopes

    They are called star polygons and share the same vertex arrangements of the convex regular polygons. In general, for any natural number n , there are regular n -pointed 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 (as such, all stellations of a ...

  6. Kepler–Poinsot polyhedron - Wikipedia

    en.wikipedia.org/wiki/Kepler–Poinsot_polyhedron

    In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra. [1] They may be obtained by stellating the regular convex dodecahedron and icosahedron, and differ from these in having regular pentagrammic faces or vertex figures. They can all be seen as three-dimensional analogues of the pentagram in one way or another.

  7. Star domain - Wikipedia

    en.wikipedia.org/wiki/Star_domain

    A star domain (equivalently, a star-convex or star-shaped set) is not necessarily convex in the ordinary sense. An annulus is not a star domain.. In geometry, a set in the Euclidean space is called a star domain (or star-convex set, star-shaped set [1] or radially convex set) if there exists an such that for all , the line segment from to lies in .

  8. Convex polygon - Wikipedia

    en.wikipedia.org/wiki/Convex_polygon

    Krein–Milman theorem: A convex polygon is the convex hull of its vertices. Thus it is fully defined by the set of its vertices, and one only needs the corners of the polygon to recover the entire polygon shape. Hyperplane separation theorem: Any two convex polygons with no points in common have a separator line. If the polygons are closed and ...

  9. Hexadecagon - Wikipedia

    en.wikipedia.org/wiki/Hexadecagon

    There are three regular star polygons, {16/3}, {16/5}, {16/7}, using the same vertices, but connecting every third, fifth or seventh points. There are also three compounds: {16/2} is reduced to 2{8} as two octagons , {16/4} is reduced to 4{4} as four squares and {16/6} reduces to 2{8/3} as two octagrams , and finally {16/8} is reduced to 8{2 ...