# Optimal packings of up to six equal circles on a triangular flat torus

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DOI: 10.1007/s00022-011-0099-6

- Cite this article as:
- Dickinson, W., Guillot, D., Keaton, A. et al. J. Geom. (2011) 102: 27. doi:10.1007/s00022-011-0099-6

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## Abstract

For each *n* between 1 and 6, we prove that a certain arrangement of *n* equal circles is the unique optimally dense packing on a standard triangular flat torus (the quotient of the plane by the lattice generated by two unit vectors with a 60^{◦} angle). The packings of 1, 2, 3, 4 and 6 circles are based on either a toroidal triangular close packing or a toroidal triangular close packing with one circle removed. The packing of 5 circles is irregular. This proves two cases of a conjecture stronger than L. Fejes Toth’s conjecture about the strong solidity of the triangular close packing on the plane.