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In geometry, a two-dimensional point group or rosette group is a group of geometric symmetries that keep at least one point fixed in a plane. Every such group is a subgroup of the orthogonal group O, including O itself. Its elements are rotations and reflections, and every such group containing only rotations is a subgroup of the special orthogonal group SO, including SO itself. That group is isomorphic to R/Z and the first unitary group, U, 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.