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In geometry, a star polygon is a type of non-convex polygon. Regular star polygons have been studied in depth; while star polygons in general appear not to have been formally defined, certain notable ones can arise through truncation operations on regular simple or star polygons.
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 dodecagram (from Greek δώδεκα (dṓdeka) 'twelve' and γραμμῆς (grammēs) 'line' [1]) is a star polygon or compound with 12 vertices. There is one regular dodecagram polygon (with Schläfli symbol {12/5} and a turning number of 5). There are also 4 regular compounds {12/2}, {12/3}, {12/4}, and {12/6}.
The regular octagonal star is very popular as a symbol of rowing clubs in the Cologne Lowland, as seen on the club flag of the Cologne Rowing Association. The geometry can be adjusted so 3 edges cross at a single point, like the Auseklis symbol An 8-point compass rose can be seen as an octagonal star, with 4 primary points, and 4 secondary points.
A regular polygon is a planar figure with all edges equal and all corners equal. A regular polyhedron is a solid (convex) figure with all faces being congruent regular polygons, the same number arranged all alike around each vertex.
A regular triangle, nonagon, and octadecagon can completely surround a point in the plane, one of 17 different combinations of regular polygons with this property. [7] However, this pattern cannot be extended to an Archimedean tiling of the plane: because the triangle and the nonagon both have an odd number of sides, neither of them can be ...
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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 n-pointed non-convex 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 .