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arXiv · 1705.02471

Periodic Steiner networks minimizing length

Jerome Alex·Karsten Grosse-Brauckmann
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Abstract

We study a problem of geometric graph theory: We determine the triply periodic graph in Euclidean 3-space which minimizes length among all graphs spanning a fundamental domain of 3-space with the same volume. The minimizer is the so-called srs network with quotient the complete graph on four vertices $K_4$. The network spans the body centred cubic lattice and is related to the gyroid triply periodic surface.

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Jerome Alex, Karsten Grosse-Brauckmann. 2017-05-06. Periodic Steiner networks minimizing length. https://arxiv.org/abs/1705.02471

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