Geometric shapes found in nature include pentagons, hexagons, spirals, waves and lines. These shapes are fascinating examples of mathematical laws being manifested by natural or biological means.

One of the most widely cited examples of geometric shapes in nature is the shell of the nautilus. The nautilus is a cephalopod that grows its shell by replicating the most recent chamber but makes the new chamber bigger than the previous one by a constant factor. This results in a logarithmic spiral that resembles those created by a Fibonacci sequence. Many other species of mollusks, like snails, build their shells in a similar way.

Other examples of Fibonacci spirals in nature are the horns of a Bighorn sheep or the spiral of an aloe plant's leaves.

A well-known geometric shape in nature is the hexagon, which is most commonly seen in the honeycomb of bees and other species of hymenoptera like wasps. Bees make use of the hexagon's ability to efficiently group together while leaving no space between adjacent cells, as would be the case if the cells were circular. The hexagonal honeycomb construction is so strong at such a light weight that it is commonly used in human manufacturing.

Continuing on the theme of six, every snowflake is unique except in one respect, which is that they all exhibit six-fold radial symmetry. Because of how water molecules crystallize when they freeze, every snowflake has six "arms."