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)
“Women over fifty already form one of the largest groups in the population structure of the western world. As long as they like themselves, they will not be an oppressed minority. In order to like themselves they must reject trivialization by others of who and what they are. A grown woman should not have to masquerade as a girl in order to remain in the land of the living.”
—Germaine Greer (b. 1939)