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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: 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]
A pentagon is a five-sided polygon. A regular pentagon has 5 equal edges and 5 equal angles. 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.
Heptagon – 7 sides; Octagon – 8 sides; Nonagon – 9 sides; Decagon – 10 sides; Hendecagon – 11 sides; Dodecagon – 12 sides; Tridecagon – 13 sides; Tetradecagon – 14 sides; Pentadecagon – 15 sides; Hexadecagon – 16 sides; Heptadecagon – 17 sides; Octadecagon – 18 sides; Enneadecagon – 19 sides; Icosagon – 20 sides ...
Prisms over the hendecagrams {11/3} and {11/4} may be used to approximate the shape of DNA molecules. [6] An 11-pointed star from the Momine Khatun Mausoleum. Fort Wood, now the base of the Statue of Liberty in New York City, is a star fort in the form of an irregular 11-point star. [7]
A triangulated polygon with 11 vertices: 11 sides and 8 diagonals form 9 triangles. Every simple polygon can be partitioned into non-overlapping triangles by a subset of its diagonals. When the polygon has n {\displaystyle n} sides, this produces n − 2 {\displaystyle n-2} triangles, separated by n − 3 {\displaystyle n-3} diagonals.
A skew zig-zag octagon has vertices alternating between two parallel planes. A regular skew octagon is vertex-transitive with equal edge lengths. In three dimensions it is a zig-zag skew octagon and can be seen in the vertices and side edges of a square antiprism with the same D 4d, [2 +,8] symmetry, order 16.
All vertices are valence-6 except the 12 centered at the original vertices which are valence 5. A geodesic polyhedron is a convex polyhedron made from triangles. They usually have icosahedral symmetry, such that they have 6 triangles at a vertex, except 12 vertices which have 5 triangles.
Let φ be the golden ratio.The 12 points given by (0, ±1, ±φ) and cyclic permutations of these coordinates are the vertices of a regular icosahedron.Its dual regular dodecahedron, whose edges intersect those of the icosahedron at right angles, has as vertices the 8 points (±1, ±1, ±1) together with the 12 points (0, ±φ, ± 1 / φ ) and cyclic permutations of these coordinates.