If symmetry is a sign of beauty, then the newly discovered Red Square nebula is one of the most beautiful objects in the universe.

But what kinds of symmetry (also called symmetry groups) might patterns or objects in three dimensions have, or even, if our minds can imagine them, might they have in higher dimensions still?

Carolyn J. MacKay, Frank R. Trechsel, Symmetrical Objects in Misantla Totonac, International Journal of American Linguistics, Vol. 74, No. 2 (April 2008), pp. 227-255 ...

The symmetries of objects can be described using fundamental ‘symmetry operations’: manipulations that leave the object looking unchanged. This is true of squares and cubes, for example, if ...

We are fascinated by symmetrical objects although artists often create minor asymmetries in their work. Source: Metropolitan Museum of Art, NYC. Public Domain. Credit: Rogers Fund, 1925.

A symmetry requires that the transformation not alter the size or shape of the object. A transformation that meets this requirement is known as an “isometry,” or a rigid motion, and the fundamental ...

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. Talk recorded 24 July 2009.

A new study finds the sedimentation of asymmetric objects in liquid is very different from that of symmetrical objects like spheres. The research may have practical applications in improving water ...