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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.
Since 13 is a prime number there is one subgroup with dihedral symmetry: Dih 1, and 2 cyclic group symmetries: Z 13, and Z 1. These 4 symmetries can be seen in 4 distinct symmetries on the tridecagon. John Conway labels these by a letter and group order. [2] Full symmetry of the regular form is r26 and no symmetry is labeled a1.
In such circumstances it is customary to drop the prefix regular. For instance, all the faces of uniform polyhedra must be regular and the faces will be described simply as triangle, square, pentagon, etc. As a corollary of the annulus chord formula, the area bounded by the circumcircle and incircle of every unit convex regular polygon is π /4
Star polygon – there are multiple types of stars Pentagram - star polygon with 5 sides; 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
A magic square is an arrangement of numbers in a square grid so that the sum of the numbers along every row, column, and diagonal is the same. Similarly, one may define a magic cube to be an arrangement of numbers in a cubical grid so that the sum of the numbers on the four space diagonals must be the same as the sum of the numbers in each row, each column, and each pillar.
A regular pentadecagon has interior angles of 156 ... there are 8 distinct symmetries. ... A regular triangle, decagon, ...
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 ...
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 .