The world turns on symmetry -- from the spin of subatomic particles to the dizzying beauty of an arabesque. But there's more to it than meets the eye. Here, Oxford mathematician Marcus du Sautoy offers a glimpse of the invisible numbers that marry all symmetrical objects. Oxford's newest science ambassador Marcus du Sautoy is also author of The Times' Sexy Maths column. He'll take you footballing with prime numbers, whopping symmetry groups, higher dimensions and other brow-furrowers.
Nature shows some incredibly intricate and surprising design elements in it's vast and breathtaking ecosystems. One of those design elements is indeed symmetry. But what do those elements have to do with our daily lives as human beings? In this inspiring talk about recent developments in biomimicry, Janine Benyus provides heartening examples of ways in which nature is already influencing the products and systems we build.
It is said that symmetry is beautiful. But is that always the case? What else is beautiful? How do we (and how should we) respond to beauty? A story, a work of art, a face, a designed object — how do we tell that something is beautiful? And why does it matter so much to us? Designer Richard Seymour explores our response to beauty and the surprising power of objects that exhibit it.
The images and text below are from this Wikipedia article on symmetry in biology.
As in the ones below, many viruses have radial symmetries, their coats being composed of a relatively small number of protein molecules arranged in a regular pattern to form polyhedrons, spheres, or ovoids. Gastroenteritis viruses: A rotavirus, B adenovirus, C norovirus, D astrovirus.

Apple cut horizontally, showing pentamerism.

Below, Volvox is a microscopic green freshwater alga with spherical symmetry. Young colonies can be seen inside the larger ones.

Below, the flower of bee orchid, Ophrys apifera is bilaterally symmetrical (zygomorphic). The lip of the flower resembles the (bilaterally symmetric) abdomen of a female bee; pollination occurs when a male bee attempts to mate with it.