Ab-initio Construction of Some Crystalline 3D Euclidean Networks
We describe a technique for construction of 3D Euclidean (E3) networks with partially-prescribed rings. The algorithm starts with 2D hyperbolic (H2) tilings, whose symmetries are commensurate with the intrinsic 2D symmetries of triply periodic minimal surfaces (or infinite periodic minimal surfaces, IPMS). The 2D hyperbolic pattern is then projected from H2 to E3, forming 3D nets. Examples of cubic and tetragonal 3-connected nets with up to 288 vertices per unit cell, each linking a pair of...[Show more]
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