Hexagon — Definition, Attributes & Examples
What is a hexagon?
In geometry, a hexagon is a six-sided polygon with six interior angles that amount to 720°, and six exterior angles that sum to 360°. Hexagons are two-dimensional shapes that can be regular, irregular, concave, convex, or complex.
Attributes of a hexagon
Every simple (non-complex) hexagon has several properties that help you identify it:
It must be a plane figure
It must enclose a space
It must have six straight sides
It must have six interior angles that each measure 120°, and sum to 720°
It must have six exterior angles that each measure 72°, and sum to 360°
| Properties of a hexagon |
|---|
| Two-dimensional Shape (Plane figure) |
| Encloses a space |
| 6 straight sides |
| 6 interior angles that sum to 720° (each measure 120) |
| 6 exterior angles that sum to 360° (each measure 120) |
Types of hexagons
A hexagon is a plane figure with six straight sides that enclose an area. This simple definition allows for several types of hexagons:
Regular
Irregular
Complex
Concave
Convex
| Regular hexagon (convex) | Irregular hexagon (convex) | Irregular hexagon (concave) | Complex hexagon |
|---|---|---|---|
 |
 |
 |
 |
The first way to separate hexagons is by identifying properties that make them regular or irregular.
Regular hexagons
Regular hexagons have six sides of equal length and six congruent interior angles. Regular hexagons can also be called equilateral hexagons, and they are always convex hexagons.
Like other regular polygons, regular hexagons enjoy several kinds of symmetry, too: they have six lines of reflection symmetry, and six rotational symmetries. All regular hexagons also have equal internal angles of 120°, central angles of 60°, and a radius equal to the length of any side.
Irregular hexagons
Irregular hexagons do not have six congruent sides and six congruent interior angles. Irregular hexagons are any six-sided, plane figures that enclose a space.
Irregular hexagons have sides of differing lengths and interior angles of varying measures. Irregular hexagons can be concave or convex. Here are two examples showing what concave and convex irregular hexagons look like:
Both hexagons pictured here are irregular, but the one on the left is convex, and the one on the right is concaved.
Convex hexagons
A convex hexagon is a hexagonal shape with no interior angle greater than 180°. Regular hexagons will always be a convex hexagon. Irregular hexagons can also be convex hexagons.
Here are two convex hexagons, one is a regular hexagon, and the other is irregular.
Notice the length of the sides of the irregular hexagon on the right. The line segment at the top of the hexagon shape is not the same as the side length at the bottom.
Concave hexagons
A concave hexagon has at least one interior angle greater than 180°. A concave hexagon will always be an irregular hexagon.
Complex hexagons
Complex hexagons are six-sided shapes that intersect themselves. The most common complex hexagon is a hexagram, also called the Star of David:
Hexagon examples
Hexagons are six-sided plane figures that have many fascinating qualities and properties, in both the natural and human worlds.
The hexagon shape is a good compromise between encompassed area and strength because it can be replicated using equilateral triangles. It tessellates readily, and for all those reasons, the hexagon shape is often used in manufacturing.
Outward-looking hexagons appear on the James Webb Space Telescope and the Extremely Large Telescope (ELT).
Regular hexagons are part of every soccer ball and the cross-section of most wooden pencils.
Nuts and bolts are usually hexagonal too. In home and business interiors, hexagonal tessellation of a floor or bathroom wall is common too.
Hexagons in real life
The natural world and the forces of physics make the hexagon shape a popular go-to polygon. Soap bubbles, beehive and honeycomb, and crystals all display hexagonal forms.
Other well-known objects using the hexagon shape include the amazing hexagon at the north pole of Saturn and the molecular structure of benzene. Snowflakes and minerals such as beryl, nepheline, and Hanksite are all found in a hexagonal pattern
Hexagonal prisms can be found in nature as well.