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Coxeter states that every zonogon (a 2m-gon whose opposite sides are parallel and of equal length) can be dissected into m(m-1)/2 parallelograms. [8] In particular this is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi.
Dual polygon: Self-dual: Area (with side length ... Example dissections for select even-sided regular polygons 2m 6 8 10 12 14 16 18 20 24 30 40 50 Image Rhombs 3 6 ...
In geometry, an octagon (from Ancient Greek ὀκτάγωνον (oktágōnon) 'eight angles') is an eight-sided polygon or 8-gon. A regular octagon has Schläfli symbol {8} [1] and can also be constructed as a quasiregular truncated square, t{4}, which alternates two types of edges.
A pentagon is a five-sided polygon. A regular pentagon has 5 equal edges and 5 equal angles. In geometry, a polygon is traditionally a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain.
A regular decagram is a 10-sided polygram, represented by symbol {10/n}, containing the same vertices as regular decagon.Only one of these polygrams, {10/3} (connecting every third point), forms a regular star polygon, but there are also three ten-vertex polygrams which can be interpreted as regular compounds:
Any straight-sided digon is regular even though it is degenerate, because its two edges are the same length and its two angles are equal (both being zero degrees). As such, the regular digon is a constructible polygon. [3] Some definitions of a polygon do not consider the digon to be a proper polygon because of its degeneracy in the Euclidean ...
[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. This decomposition is based on a Petrie polygon projection of an 8-cube, with 28 of 1792 faces.
A regular polygon with n sides can be constructed with ruler, compass, and angle trisector if and only if =, where r, s, k ≥ 0 and where the p i are distinct Pierpont primes greater than 3 (primes of the form +). [8]: Thm. 2 These polygons are exactly the regular polygons that can be constructed with Conic section, and the regular polygons ...