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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.
Quadrilateral – 4 sides Cyclic quadrilateral; Kite. ... Decagon – 10 sides; ... Megagon - 1,000,000 sides; Star polygon – there are multiple types of stars
Note 2: In a kite, one diagonal bisects the other. The most general kite has unequal diagonals, but there is an infinite number of (non-similar) kites in which the diagonals are equal in length (and the kites are not any other named quadrilateral).
More generally, if the quadrilateral is a rectangle with sides a and b and diagonal d then Ptolemy's theorem reduces to the Pythagorean theorem. In this case the center of the circle coincides with the point of intersection of the diagonals. The product of the diagonals is then d 2, the right hand side of Ptolemy's relation is the sum a 2 + b 2.
The six lines of a complete quadrangle meet in pairs to form three additional points called the diagonal points of the quadrangle. Similarly, among the six points of a complete quadrilateral there are three pairs of points that are not already connected by lines; the line segments connecting these pairs are called diagonals. For points and ...
[4] In particular this is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi. For the regular hexadecagon , m =8, and it can be divided into 28: 4 squares and 3 sets of 8 rhombs.
There are three regular star polygons: {15/2}, {15/4}, {15/7}, constructed from the same 15 vertices of a regular pentadecagon, but connected by skipping every second, fourth, or seventh vertex respectively.
The polytopes of rank 2 (2-polytopes) are called polygons.Regular polygons are equilateral and cyclic.A p-gonal regular polygon is represented by Schläfli symbol {p}.. Many sources only consider convex polygons, but star polygons, like the pentagram, when considered, can also be regular.