# Hexagon

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

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) × s**, or approximately^{2}**2.5980762 × s**(where s=side length)^{2} - 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.