Geometrical Relationships between Nets Mapped on Isomorphic Quotient Graphs: Examples

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The point group of a three-periodic net is generally isomorphic to a subgroup of the automorphism group of its quotient graph. Emphasis is given to then-periodic net of maximal symmetry whose point group is isomorphic to the automorphism group. These characteristic nets, which are unique up to isomorphism, have been determined for the following graphs: K(2)3, 2K2∪2K(3)2, C(2)4, K(2)2+K(2)2, K2(6),4(3), and AP4. It is shown that the topology of three-periodic nets admitting these graphs as their quotient graph is generated by orthogonal projection of the net of maximal symmetry.