# Hexagon

A hexagon is a 6-sided polygon (a flat shape with straight sides):

images/area-coords.js?mode=6

Soap bubbles tend to form hexagons
when they join up.

Honeycomb has hexagons too!

## Regular or Irregular

When all angles are equal and all sides are equal it is regular, otherwise it is irregular:

 Regular Hexagon Irregular Hexagons

## Concave or Convex

A convex hexagon has no angles pointing inwards. More precisely, no internal angles can be more than 180°.

When any internal angle is greater than 180° it is concave. (Think: concave has a "cave" in it)

 Convex Hexagon Concave Hexagon

## Is it a Hexagon?

No curved sides. And the shape must also be closed (all the lines connect up):

 Hexagon (straight sides) Not a Hexagon (has a curve) Not a Hexagon (open, not closed)

## Properties

A regular hexagon has:

• Interior Angles of 120°
• Exterior Angles of 60°
• Area = (1.5√3) × s2 , or approximately 2.5980762 × s2 (where s=side length)
• Radius equals side length

The radius is the side length.
It is also made of 6 regular triangles!

Any hexagon has:

• Sum of Interior Angles of 720°
• 9 diagonals

## More Images

Hexagonal nuts and bolts are easy to grip with a wrench,
which can be re-positioned every 60° if needed.

There is a huge hexagon on Saturn,
it is wider than Earth.

Another image of the hexagon on Saturn.

Snowflakes have hexagonal patterns, like this beautiful image from NASA.
Photograph by NASA / Alexey Kljatov.

Also a snowflake!
Photograph by NASA / Alexey Kljatov.

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