Cool Wallpapers: Geometric Wallpaper

Thursday, June 28, 2012

Geometric Wallpaper

In geometry, a two-dimensional point group or rosette group is a group of geometric symmetries (isometries) that keep at least one point fixed in a plane. Every such group is a subgroup of the orthogonal group O(2), including O(2) itself. Its elements are rotations and reflections, and every such group containing only rotations is a subgroup of the special orthogonal group SO(2), including SO(2) itself. That group is isomorphic to R/Z and the first unitary group, U(1), a group also known as the circle group. The two-dimensional point groups are important as a basis for the axial three-dimensional point groups, with the addition of reflections in the axial coordinate. They are also important in symmetries of organisms, like starfish and jellyfish, and organism parts, like flowers.