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The regular decagon has Dih 10 symmetry, order 20. There are 3 subgroup dihedral symmetries: Dih 5, Dih 2, and Dih 1, and 4 cyclic group symmetries: Z 10, Z 5, Z 2, and Z 1. These 8 symmetries can be seen in 10 distinct symmetries on the decagon, a larger number because the lines of reflections can either pass through vertices or edges.
A simplicial arrangement formed by 20 lines, the sides and symmetry axes of a regular decagon. Adding the line at infinity produces another simplicial arrangement with 21 lines. An arrangement of lines in the projective plane is said to be simplicial if every cell of the arrangement is
A regular dodecagon is a figure with sides of the same length and internal angles of the same size. It has twelve lines of reflective symmetry and rotational symmetry of order 12. A regular dodecagon is represented by the Schläfli symbol {12} and can be constructed as a truncated hexagon, t{6}, or a twice-truncated triangle, tt{3}. The ...
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 ...
The symmetries of a regular pentadecagon as shown with colors on edges and vertices. Lines of reflections are blue. Gyrations are given as numbers in the center. Vertices are colored by their symmetry positions. The regular pentadecagon has Dih 15 dihedral symmetry, order 30, represented by 15 lines of
The regular hexadecagon has Dih 16 symmetry, order 32. There are 4 dihedral subgroups: Dih 8, Dih 4, Dih 2, and Dih 1, and 5 cyclic subgroups: Z 16, Z 8, Z 4, Z 2, and Z 1, the last implying no symmetry. On the regular hexadecagon, there are 14 distinct symmetries. John Conway labels full symmetry as r32 and no symmetry is labeled a1.
Symmetries of a regular tridecagon. Vertices are colored by their symmetry positions. Blue mirrors are drawn through vertices and edge. Gyration orders are given in the center. The regular tridecagon has Dih 13 symmetry, order 26. Since 13 is a prime number there is one subgroup with dihedral symmetry: Dih 1, and 2 cyclic group symmetries: Z 13 ...
Full symmetry of the regular form is r36 and no symmetry is labeled a1. The dihedral symmetries are divided depending on whether they pass through vertices (d for diagonal) or edges (p for perpendiculars), and i when reflection lines path through both edges and vertices.