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In particular this is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi. For the regular decagon, m=5, and it can be divided into 10 rhombs, with examples shown below. This decomposition can be seen as 10 of 80 faces in a Petrie polygon projection plane of the 5-cube.
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 polytope is a geometric object with flat sides, which exists in any general number of dimensions. The following list of polygons, polyhedra and polytopes gives the names of various classes of polytopes and lists some specific examples.
A decomino, or 10-omino, is a polyomino of order 10; that is, a polygon in the plane made of 10 equal-sized squares connected edge to edge. [1] When rotations and reflections are not considered to be distinct shapes, there are 4,655 different free decominoes (the free decominoes comprise 195 with holes and 4,460 without holes).
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; Hendecagram - star polygon with 11 sides; Dodecagram - star ...
Some regular polygons are easy to construct with compass and straightedge; other regular polygons are not constructible at all. The ancient Greek mathematicians knew how to construct a regular polygon with 3, 4, or 5 sides, [11]: p. xi and they knew how to construct a regular polygon with double the number of sides of a given regular polygon.
The white polygon lines represent the "vertex figure" polygon. The colored faces are included on the vertex figure images help see their relations. Some of the intersecting faces are drawn visually incorrectly because they are not properly intersected visually to show which portions are in front.
For any two simple polygons of equal area, the Bolyai–Gerwien theorem asserts that the first can be cut into polygonal pieces which can be reassembled to form the second polygon. The lengths of the sides of a polygon do not in general determine its area. [9] However, if the polygon is simple and cyclic then the sides do determine the area. [10]