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In geometry, a polygon is traditionally a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain. These segments are called its edges or sides, and the points where two of the edges meet are the polygon's vertices (singular: vertex) or corners.
The following list of polygons, polyhedra and polytopes gives the names of various classes of polytopes and lists some specific examples. Polytope elements [ edit ]
Since 11 is a prime number there is one subgroup with dihedral symmetry: Dih 1, and 2 cyclic group symmetries: Z 11, and Z 1. These 4 symmetries can be seen in 4 distinct symmetries on the hendecagon. John Conway labels these by a letter and group order. [11] Full symmetry of the regular form is r22 and no symmetry is labeled a1.
As with all odd regular polygons and star polygons whose orders are not products of distinct Fermat primes, the regular hendecagrams cannot be constructed with compass and straightedge. [4] However, Hilton & Pedersen (1986) describe folding patterns for making the hendecagrams {11/3}, {11/4}, and {11/5} out of strips of paper.
In recreational mathematics, a polyform is a plane figure constructed by joining together identical basic polygons. The basic polygon is often (but not necessarily) a convex plane-filling polygon, such as a square or a triangle. More specific names have been given to polyforms resulting from specific basic polygons, as detailed in the table below.
Skew polygons can be created via the blending operation. The blend of two polygons P and Q, written P#Q, can be constructed as follows: take the cartesian product of their vertices V P × V Q. add edges (p 0 × q 0, p 1 × q 1) where (p 0, p 1) is an edge of P and (q 0, q 1) is an edge of Q. select an arbitrary connected component of the result.
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In geometry, a convex polyhedron whose faces are regular polygons is known as a Johnson solid, or sometimes as a Johnson–Zalgaller solid [1].Some authors exclude uniform polyhedra (in which all vertices are symmetric to each other) from the definition; uniform polyhedra include Platonic and Archimedean solids as well as prisms and antiprisms. [2]