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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}.
Example equiangular polygons Direct Indirect Skew A rectangle, <4>, is a convex direct equiangular polygon, containing four 90° internal angles.: A concave indirect equiangular polygon, <6-2>, like this hexagon, counterclockwise, has five left turns and one right turn, like this tetromino.
A regular skew hexagon seen as edges (black) of a triangular antiprism, symmetry D 3d, [2 +,6], (2*3), order 12. A skew hexagon is a skew polygon with six vertices and edges but not existing on the same plane. The interior of such a hexagon is not generally defined. A skew zig-zag hexagon has vertices alternating between two parallel planes.
The polygon is the convex hull of its edges. Additional properties of convex polygons include: The intersection of two convex polygons is a convex polygon. A convex polygon may be triangulated in linear time through a fan triangulation, consisting in adding diagonals from one vertex to all other vertices.
All convex polygons are simple. Concave: Non-convex and simple. There is at least one interior angle greater than 180°. Star-shaped: the whole interior is visible from at least one point, without crossing any edge. The polygon must be simple, and may be convex or concave. All convex polygons are star-shaped.
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 ...
The classical convex polytopes may be considered tessellations, or tilings, of spherical space. Tessellations of euclidean and hyperbolic space may also be considered regular polytopes. Tessellations of euclidean and hyperbolic space may also be considered regular polytopes.
There are 17 combinations of regular convex polygons that form 21 types of plane-vertex tilings. [ 6 ] [ 7 ] Polygons in these meet at a point with no gap or overlap. Listing by their vertex figures , one has 6 polygons, three have 5 polygons, seven have 4 polygons, and ten have 3 polygons.