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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 regular pentadecagon has interior angles of 156 ... there are 8 distinct symmetries. ... decagon, and pentadecagon can ...
There are 3 subgroup dihedral symmetries: Dih 7, Dih 2, and Dih 1, and 4 cyclic group symmetries: Z 14, Z 7, Z 2, and Z 1. These 8 symmetries can be seen in 10 distinct symmetries on the tetradecagon, a larger number because the lines of reflections can either pass through vertices or edges. John Conway labels these by a letter and group order. [4]
Since 17 is a prime number there is one subgroup with dihedral symmetry: Dih 1, and 2 cyclic group symmetries: Z 17, and Z 1. These 4 symmetries can be seen in 4 distinct symmetries on the heptadecagon. John Conway labels these by a letter and group order. [7] Full symmetry of the regular form is r34 and no symmetry is labeled a1.
There are three regular star polygons, {16/3}, {16/5}, {16/7}, using the same vertices, but connecting every third, fifth or seventh points. There are also three compounds: {16/2} is reduced to 2{8} as two octagons , {16/4} is reduced to 4{4} as four squares and {16/6} reduces to 2{8/3} as two octagrams , and finally {16/8} is reduced to 8{2 ...
The diagonals divide the polygon into 1, 4, 11, 24, ... pieces. [ a ] For a regular n -gon inscribed in a circle of radius 1 {\displaystyle 1} , the product of the distances from a given vertex to all other vertices (including adjacent vertices and vertices connected by a diagonal) equals n .
There is one regular star polygon: {12/5}, using the same vertices, but connecting every fifth point. There are also three compounds: {12/2} is reduced to 2{6} as two hexagons , and {12/3} is reduced to 3{4} as three squares , {12/4} is reduced to 4{3} as four triangles, and {12/6} is reduced to 6{2} as six degenerate digons .
The regular icosagon has Schläfli symbol {20}, and can also be constructed as a truncated decagon, t{10}, or a twice-truncated pentagon, tt{5}. One interior angle in a regular icosagon is 162°, meaning that one exterior angle would be 18°. The area of a regular icosagon with edge length t is