Definition of crashed polygon - What is it, Meaning and Concept

A polygon is a figure composed of a certain number of sides, which are non-aligned and straight segments.Depending on their characteristics, there are multiple classifications of the polygons.

The concave polygons are those that have at least one interior angle that measures more than 180 ° or pi radians.Within this group, are the starry polygons , characterized by its star form.

A crashed polygon, therefore, is concave since it has one or more interior angles of more than 180 ° or pi radians.Other characteristics characteristic of concave polygons and crashed polygons they also have one or more external diagonals and have two or more vertices that, when joined by a segment, cut at least one side of the figure .

A crashed polygon is not only concave, but it can also be part of the regular polygons when its interior angles and its sides are equal.Through certain "unions" made using new segments that link the vertices, a star polygon can be created from a regular polygon (such as a pentagon, for example).

The regular star polygons , in addition, can be simple.This happens when their vertices are, alternatively, on a pair of concentric circles and with central angles that are the same.

One way to build starry polygons is through the overlay and the turn of other polygons.It is possible to develop numerous star-shaped polygons, such as the famous Star of David , which is a symbol of the religion Jewish .

By dividing a circumference into n parts and joining them in succession it is possible to obtain a regular convex polygon; if the joints between the vertices are made two by two, three by three, etc., a concave and crashed polygon is obtained.In other words, to construct a starry polygon you can start from a regular convex one and join its vertices in sequence continue to maintain the interval between one and the other, so that the following conditions are met:

* the number of vertices of the original polygon ( N ) over the space between one ( M ) must form a fraction irreducible, that is, that its denominator and numerator have no common factors, so the fraction cannot be simplified;

* the starry polygon that is formed by joining the vertices of a regular convex polygon must be the same regardless of the direction in which the segments are drawn.In other words, N/M and N/(NM) must represent the same polygon.

Some concepts related to the crashed polygon are the following: gener , the number of sides (or ropes) it has, which must match its number of vertices , which is why its denomination is the same as that of convex polygons (with a genus 6 we speak of starry hexagon , for example); step , the number of parts into which the circumference is divided, and the value that comprises the sides of the polygon; species , a property with ordinal denomination that refers to the step, such that if the unions are two at a time there is talk of second species , and so on.

Of the best known polygons, it is known that the triangle and the square do not have a crashed one; the pentagon, the octagon, the decagon and the dodecagon, on the other hand, have one each, first, second, second and fifth or fourth species, respectively; heptagono and eneagono have two each, of first and second species; The eleven side, finally, has four, ranging from first to fourth species .