Fundamental Domain
The fundamental domain of a point group is a conic solid. An object with a given symmetry in a given orientation is characterized by the fundamental domain. If the object is a surface it is characterized by a surface in the fundamental domain continuing to its radial bordal faces or surface. If the copies of the surface do not fit, radial faces or surfaces can be added. They fit anyway if the fundamental domain is bounded by reflection planes.
For a polyhedron this surface in the fundamental domain can be part of an arbitrary plane. For example, in the disdyakis triacontahedron one full face is a fundamental domain. Adjusting the orientation of the plane gives various possibilities of combining two or more adjacent faces to one, giving various other polyhedra with the same symmetry. The polyhedron is convex if the surface fits to its copies and the radial line perpendicular to the plane is in the fundamental domain.
Also the surface in the fundamental domain may be composed of multiple faces.
Read more about this topic: Point Groups In Three Dimensions
Famous quotes containing the words fundamental and/or domain:
“Our species successfully raised children for tens of thousands of years before the first person wrote down the word “psychology.” The fundamental skills needed to be a parent are within us. All we’re really doing is fine-tuning a process that’s already remarkably successful.”
—Lawrence Kutner (20th century)
“Every sign is subject to the criteria of ideological evaluation.... The domain of ideology coincides with the domain of signs. They equate with one another. Wherever a sign is present, ideology is present, too. Everything ideological possesses semiotic value.”
—V.N. (Valintin Nikolaevic)