Periodic structures can give outstanding mechanical/dynamical.
It really depends how to construct the structure. Theoretically speaking, as long as your overall structure can be considered as assembled by repeating a fundamental building block many times (say 10 or more) in a certain direction, that direction can be considered as periodic. It is very possible that you repeat in-plane but not necessary repeat many times through the thickness, then the thickness direction is not periodic. My recent discovery of Mechanics of Structure Genome can provide an easy treatment of this type of structure. Register for the webinar https://www.nafems.org/events/nafems/2017/multiscalefeb2017/ for more details of MSG. Feel free to try the corresponding code SwiftComp on cdmHUB: https://cdmhub.org/resources/scstandard.
Technically, a two-dimensional honeycomb is not a Bravais lattice. It can however be represented as a two-dimensional triangular Bravais lattice. For details, you may wish to consult Sec. 2.6 of the book Principles of condensed matter physics, by PM Chaikin, and TC Lubensky (Cambridge University Press, 2000).
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