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In geometry, a nonagon (/ ˈ n ɒ n ə ɡ ɒ n /) or enneagon (/ ˈ ɛ n i ə ɡ ɒ n /) is a nine-sided polygon or 9-gon. The name nonagon is a prefix hybrid formation , from Latin ( nonus , "ninth" + gonon ), used equivalently, attested already in the 16th century in French nonogone and in English from the 17th century.
In mathematics, a dihedral group is the group of symmetries of a regular polygon, [1] [2] which includes rotations and reflections. Dihedral groups are among the simplest examples of finite groups, and they play an important role in group theory, geometry, and chemistry. [3] The notation for the dihedral group differs in geometry and abstract ...
There are 3 types of dihedral symmetry in three dimensions, each shown below in 3 notations: Schönflies notation, Coxeter notation, and orbifold notation. Chiral. D n, [n,2] +, (22n) of order 2n – dihedral symmetry or para-n-gonal group (abstract group: Dih n). Achiral
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.
All of the discrete point symmetries are subgroups of certain continuous symmetries. They can be classified as products of orthogonal groups O(n) or special orthogonal groups SO(n). O(1) is a single orthogonal reflection, dihedral symmetry order 2, Dih 1. SO(1) is just the identity. Half turns, C 2, are needed to complete.
In geometry, the Rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces. It has a total of 62 faces: 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, with 60 vertices , and 120 edges .
The other two, the dihedral group of order 8 and the quaternion group, are not. [3] The dihedral group of order 8 is isomorphic to the permutation group generated by (1234) and (13). The numbers in this table come from numbering the 4! = 24 permutations of S 4, which Dih 4 is a subgroup of, from 0 (shown as a black circle) to 23.
(Increasing any of the numbers defining a hyperbolic or Euclidean tiling makes another hyperbolic tiling.) Point groups: (p 2 2) dihedral symmetry, =,, … (order ) (3 3 2) tetrahedral symmetry (order 24) (4 3 2) octahedral symmetry (order 48) (5 3 2) icosahedral symmetry (order 120)