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Mirror Symmetry


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_1=s-2n^^(s·n^^)

whenever it contains s. The vector s_1 is the mirror image of s about W.

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, Chiral, Enantiomer, Handedness, Mirror Image, Reflection, Symmetry

Portions of this entry contributed by David Terr

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Cite this as:

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

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