Star polygon in the context of "Isotoxal"

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⭐ Core Definition: Star polygon

In geometry, a star polygon is a type of non-convex polygon. Regular star polygons have been studied in depth; while star polygons in general appear not to have been formally defined, certain notable ones can arise through truncation operations on regular simple or star polygons.

Branko Grünbaum identified two primary usages of this terminology by Johannes Kepler, one corresponding to the regular star polygons with intersecting edges that do not generate new vertices, and the other one to the isotoxal concave simple polygons.

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Star polygon in the context of Starfish

Starfish or sea stars are a class of marine invertebrates generally shaped like a star polygon. (In common usage, these names are also often applied to ophiuroids, which are correctly referred to as brittle stars or basket stars.) Starfish are also known as asteroids because they form the taxonomic class Asteroidea (/ˌæstəˈrɔɪdiə/). About 1,900 species of starfish live on the seabed, and are found in all the world's oceans, from warm, tropical zones to frigid, polar regions. They can occur from the intertidal zone down to abyssal depths, at 6,000 m (20,000 ft) below the surface.

Starfish are echinoderms and typically have a central disc and usually five arms, though some species have a larger number of arms. The aboral or upper surface may be smooth, granular or spiny, and is covered with overlapping plates. Many species are brightly coloured in various shades of red or orange, while others are blue, grey or brown. Starfish have tube feet operated by a hydraulic system and a mouth at the centre of the oral or lower surface. They are opportunistic feeders and are mostly predators on benthic invertebrates. Several species have specialized feeding behaviours including eversion of their stomachs and suspension feeding. They have complex life cycles and can reproduce both sexually and asexually. Most can regenerate damaged parts or lost arms and they can shed arms as a means of defense.

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Star polygon in the context of Regular polygons

In Euclidean geometry, a regular polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be either convex or star. In the limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter or area is fixed, or a regular apeirogon (effectively a straight line), if the edge length is fixed.

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Star polygon in the context of Pentagon

In geometry, a pentagon (from Greek πέντε (pente) 'five' and γωνία (gonia) 'angle') is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°.

A pentagon may be simple or self-intersecting. A self-intersecting regular pentagon (or star pentagon) is called a pentagram.

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Star polygon in the context of Star (heraldry)

In heraldry, the term star may refer to any star-shaped charge with any number of rays, which may appear straight or wavy, and may or may not be pierced. While there has been much confusion between the two due to their similar shape, a star with straight-sided rays is usually called a mullet in English heraldry, while one with wavy rays is usually called an estoile.

While a mullet may have any number of points, it is presumed to have five unless otherwise specified in the blazon, and pierced mullets are common; estoiles, however, are presumed to have six rays and (as of 1909) had not been found pierced. In Scottish heraldry, an estoile is the same as in English heraldry, but mullet refers only to a mullet pierced (also called a spur revel), while one that is not pierced is called a star.

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Star polygon in the context of Decagram (geometry)

In geometry, a decagram is a 10-point star polygon. There is one regular decagram, containing the vertices of a regular decagon, but connected by every third point. Its Schläfli symbol is {10/3}.

The name decagram combines a numeral prefix, deca-, with the Greek suffix -gram. The -gram suffix derives from γραμμῆς (grammēs) meaning a line.

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