Minimal nets and minimal minimal surfaces

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The 3-periodic nets of genus 3 ('minimal nets') are reviewed and their symmetries re-examined. Although they are all crystallographic, seven of the 15 only have maximum-symmetry embeddings if some links are allowed to have zero length. The connection between the minimal nets and the genus-3 zero-mean-curvature surfaces ('minimal minimal' surfaces) is explored by determining the surface associated with a net that has a self-dual tiling. The fact that there are only five such surfaces but 15 minimal nets is rationalized by showing that all the minimal nets can serve as the labyrinth graph of one of the known minimal minimal surfaces.
Publisher
WILEY-BLACKWELL
Issue Date
2013-09
Language
English
Article Type
Article
Keywords

3-PERIODIC NETS; PERIODIC GRAPHS; CRYSTAL NETS; TILINGS; CHEMISTRY; SYMMETRY; GEOMETRY

Citation

ACTA CRYSTALLOGRAPHICA SECTION A, v.69, pp.483 - 489

ISSN
0108-7673
DOI
10.1107/S0108767313018370
URI
http://hdl.handle.net/10203/254712
Appears in Collection
RIMS Journal Papers
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