Chirality and Symmetry Group
A figure is achiral if and only if its symmetry group contains at least one orientation-reversing isometry. (In Euclidean geometry any isometry can be written as with an orthogonal matrix and a vector . The determinant of is either 1 or −1 then. If it is −1 the isometry is orientation-reversing, otherwise it is orientation-preserving.)
Read more about this topic: Chirality (mathematics)
Famous quotes containing the words symmetry and/or group:
“What makes a regiment of soldiers a more noble object of view than the same mass of mob? Their arms, their dresses, their banners, and the art and artificial symmetry of their position and movements.”
—George Gordon Noel Byron (1788–1824)
“I can’t think of a single supposedly Black issue that hasn’t wasted the original Black target group and then spread like the measles to outlying white experience.”
—June Jordan (b. 1936)