Slide shows of triply periodic surfaces with cubic space groups

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  Balanced minimal surfaces

A variety of views of the 24 triply periodic minimal balance surfaces that have cubic space groups and generating units bounded by straight edges (explained and illustrated on the the previous page    ), together with some others that don't fit this category. [83 slides]

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  Non-balanced minimal surfaces

These minimal surfaces have non-congruent labyrinths. They come in a wide variety. [53 slides]

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  Non-minimal triply periodic surfaces

Minimal surfaces are surfaces of zero mean curvature. In cases where a minimal surface with a given symmetry and topology does not exist, the software Surface Evolver can find non-minimal varieties of various kinds (e.g. surfaces of constant mean curvature or surfaces that minimise integrated squared curvature). [23 slides]


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  Nodal surfaces

A triply periodic function F has a Fourier expansion which represents it as a sum of plane waves. If Fijk is a plane wave in the direction [ijk], then for a given symmetry a summation over all symmetrically-equivalent ijk will produce a nodal surface fijk = 0 and level surfaces fijk = constant, with that symmetry. The minimal surfaces can be approximated quite closely by nodal surfaces with the same symmetry and topology. (See von Schnering & Nesper, Z. Phys. B: Condens. Mat. 83 (1991) 407-12) [36 slides]

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