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Symmetries of a regular hendecagon. Vertices are colored by their symmetry positions. Blue mirror lines are drawn through vertices and edge. Gyration orders are given in the center. The regular hendecagon has Dih 11 symmetry, order 22. Since 11 is a prime number there is one subgroup with dihedral symmetry: Dih 1, and 2 cyclic group symmetries ...
Individual polygons are named (and sometimes classified) according to the number of sides, combining a Greek-derived numerical prefix with the suffix -gon, e.g. pentagon, dodecagon. The triangle, quadrilateral and nonagon are exceptions, although the regular forms trigon, tetragon, and enneagon are sometimes encountered as well.
Some regular polygons are easy to construct with compass and straightedge; other regular polygons are not constructible at all. The ancient Greek mathematicians knew how to construct a regular polygon with 3, 4, or 5 sides, [11]: p. xi and they knew how to construct a regular polygon with double the number of sides of a given regular polygon.
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. [5]
A polytope is a geometric object with flat sides, which exists in any general number of dimensions. ... 11-cell, 57-cell; Regular star 4-polytope. ... Regular polygon ...
Hexagram – star polygon with 6 sides Star of David (example) Heptagram – star polygon with 7 sides; Octagram – star polygon with 8 sides Star of Lakshmi (example) Enneagram - star polygon with 9 sides; Decagram - star polygon with 10 sides; Hendecagram - star polygon with 11 sides; Dodecagram - star polygon with 12 sides; Apeirogon ...
For any two simple polygons of equal area, the Bolyai–Gerwien theorem asserts that the first can be cut into polygonal pieces which can be reassembled to form the second polygon. The lengths of the sides of a polygon do not in general determine its area. [9] However, if the polygon is simple and cyclic then the sides do determine the area. [10]
Some regular polygons are easy to construct with compass and straightedge; others are not. The ancient Greek mathematicians knew how to construct a regular polygon with 3, 4, or 5 sides, [1]: p. xi and they knew how to construct a regular polygon with double the number of sides of a given regular polygon. [1]: pp. 49–50 This led to the ...