Polytopes Without Mirror Symmetry
Many polytopes lack mirror symmetry, and in that sense form chiral polytopes. The simplest example is a scalene triangle.
It is possible for polytopes to have a high degree of symmetry, but yet to lack mirror symmetry; an example is the snub cube, which is vertex-transitive and chiral in this sense.
Read more about this topic: Chiral Polytope
Famous quotes containing the words mirror and/or symmetry:
“The barriers of conventionality have been raised so high, and so strangely cemented by long existence, that the only hope of overthrowing them exists in the union of numbers linked together by common opinion and effort ... the united watchword of thousands would strike at the foundation of the false system and annihilate it.”
—Mme. Ellen Louise Demorest 18241898, U.S. womens magazine editor and womans club movement pioneer. Demorests Illustrated Monthly and Mirror of Fashions, p. 203 (January 1870)
“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 (17881824)