Symmetry Groups
In 2D the group D3 is the symmetry group of an equilateral triangle. In contrast with the case of a square or other polygon, all permutations of the vertices can be achieved by rotation and flipping over (or reflecting).
In 3D there are two different symmetry groups which are algebraically the group D3:
- one with a 3-fold rotation axis and a perpendicular 2-fold rotation axis (hence three of these): D3
- one with a 3-fold rotation axis in a plane of reflection (and hence also in two other planes of reflection): C3v
Read more about this topic: Dihedral Group Of Order 6
Famous quotes containing the words symmetry and/or groups:
“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)
“Writers and politicians are natural rivals. Both groups try to make the world in their own images; they fight for the same territory.”
—Salman Rushdie (b. 1947)