Three-dimensional Euclidean nets from two-dimensional hyperbolic tilings: kaleidoscopic examples
We present a method for geometric construction of periodic three-dimensional Euclidean nets by projecting two-dimensional hyperbolic tilings onto a family of triply periodic minimal surfaces (TPMSs). Our techniques extend the combinatorial tiling theory of Dress, Huson & Delgado-Friedrichs to enumerate simple reticulations of these TPMSs. We include a taxonomy of all networks arising from kaleidoscopic hyperbolic tilings with up to two distinct tile types (and their duals, with two distinct...[Show more]
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|Source:||Acta Crystallographica Section A: Foundations of Crystallography|
|01_Ramsden_Three-dimensional_Euclidean_2009.pdf||4.31 MB||Adobe PDF||Request a copy|
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