TOPICS
Search

Mirror Symmetry


MirrorSymmetry

Let V=R^k be a k-dimensional vector space over R, let S subset V, and let

 W={w in V:w·n^^=0}

be a subspace of V of dimension k-1, where n^^ is a unit normal vector of W. Then S is said to have mirror symmetry about W if S contains the vector

 s^'=s-2n^^(s·n^^)

whenever it contains s. The vector s^' is the mirror image of s about W. For a plane figure, k=2 and the subspace W is a line called an axis of symmetry. For a geometric object in three-dimensional space, such as a surface or solid, k=3 and W is a plane of symmetry.

Mirror symmetry is sometimes called bilateral symmetry. Most animals are very nearly bilaterally symmetric. Molecules without bilateral symmetry come in two varieties denoted L (laevo) and R (dextro), each of which is the mirror image of the other. Such images are called enantiomers, and their property of being the same except by reflection is called handedness. Some highly symmetric geometric solids, including the snub cube and snub dodecahedron, also lack mirror symmetry and come in two enantiomorphous forms.


See also

Amphichiral, Axis of Symmetry, Bilateral Symmetry, Chiral, Enantiomer, Handedness, Mirror Image, Plane of Symmetry, Reflection, Symmetry

Portions of this entry contributed by David Terr

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W., with contributions by David Terr. "Mirror Symmetry." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MirrorSymmetry.html

Subject classifications