What is a hexagon?

In geometry, a hexagon is a six-sided polygon v six inner angles that amount come 720°, and six exterior angle that sum to 360°. Hexagons room two-dimensional forms that deserve to be regular, irregular, concave, convex, or complex.

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Attributes the a hexagon

Every straightforward (non-complex) hexagon has actually several properties that assist you determine it:

It need to be a aircraft figureIt must enclose a spaceIt must have actually six directly sidesIt must have actually six internal angles that each measure 120°, and sum come 720°It must have actually six exterior angle that each measure up 72°, and sum to 360°

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Properties the a hexagon
Two-dimensional shape (Plane figure)
Encloses a space
6 directly sides
6 internal angles that amount to 720° (each measure 120°)
6 exterior angles that sum to 360° (each measure 72°)

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Types

Types the hexagons

A hexagon is a plane figure with 6 straight sides the enclose an area. This simple definition allows for several species of hexagons:

RegularIrregularComplexConcaveConvexDifferent hexagon shapesRegular hexagon (convex)Irregular hexagon (convex)Irregular hexagon (concave)Complex hexagon
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The very first way to separate hexagons is by identifying properties the make them consistent or irregular.

Regular hexagons

Regular hexagons have six sides of same length and six congruent internal angles. Continual hexagons can likewise be referred to as equilateral hexagons, and also they are constantly convex hexagons.

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Like other consistent polygons, continual hexagons reap several kinds of symmetry, too: they have actually six currently of enjoy symmetry, and six rotational symmetries. All regular hexagons additionally have equal inner angles of 120°, central angles the 60°, and a radius same to the size of any type of side.

Irregular hexagons

Irregular hexagons carry out not have six congruent sides and six congruent internal angles. Irregular hexagons are any type of six-sided, airplane figures the enclose a space.

Irregular hexagons have sides of differing lengths and interior angles of varying measures. Rarely often, rarely hexagons have the right to be concave or convex. Here are two examples showing what concave and also convex rarely often rare hexagons watch like:

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Both hexagons pictured below are irregular, yet the one ~ above the left is convex, and also the one ~ above the best is concaved.

Convex hexagons

A convex hexagon is a hexagonal shape with no internal angle greater than 180°. Regular hexagons will always be a convex hexagon. Rarely often, rarely hexagons can likewise be convex hexagons.

Here room two convex hexagons, one is a continual hexagon, and also the various other is irregular.

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Notice the size of the political parties of the rarely often rare hexagon top top the right. The line segment at the height of the hexagon form is not the very same as the side length at the bottom.

Concave hexagons

A concave hexagon contends least one interior angle better than 180°. A concave hexagon will always be an rarely often rare hexagon.

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Complex Hexagons

Complex hexagons are six-sided shapes that crossing themselves. The many common complex hexagon is a hexagram, also called the Star the David:

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Hexagon examples

Hexagons space six-sided aircraft figures that have many fascinating qualities and properties, in both the natural and human worlds.

The hexagon shape is a great compromise between encompassed area and strength due to the fact that it can be replicated utilizing equilateral triangles. That tessellates readily, and for all those reasons, the hexagon form is often used in manufacturing.

Outward-looking hexagons appear on the James Webb an are Telescope and also the Extremely large Telescope (ELT).

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Regular hexagons are component of every football ball and also the cross-section of many wooden pencils.

Nuts and bolts room usually hexagonal too. In home and business interiors, hexagonal tessellation the a floor or bathroom wall is common too.

Hexagons in actual life

The natural world and also the pressures of physics do the hexagon shape a well-known go-to polygon. Soap bubbles, beehive and also honeycomb, and crystals all display screen hexagonal forms.

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Other renowned objects making use of the hexagon shape incorporate the exceptional hexagon in ~ the north pole of Saturn and also the molecular structure of benzene. Snowflakes and minerals such as beryl, nepheline, and Hanksite space all discovered in a hexagonal pattern

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Hexagonal prisms have the right to be discovered in nature together well.

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