Journal
DISCRETE & COMPUTATIONAL GEOMETRY
Volume 33, Issue 1, Pages 67-81Publisher
SPRINGER
DOI: 10.1007/s00454-004-1147-x
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We study realizations of periodic graphs in Euclidean spaces with each vertex in the center of gravity of its neighbors. As a first application, we show that every planar, 3-connected, 2-periodic graph can be drawn into the plane wit h convex faces such that the drawing realizes every combinatorial automorphism of the graph as an isometric symmetry. This extends results by Thomassen and by Mani-Levitska, Guigas, and Klee.
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