caa a22 4500 445813350 CHVBK 20180317145218.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00022-011-0099-6 doi (NATIONALLICENCE)springer-10.1007/s00022-011-0099-6 Optimal packings of up to six equal circles on a triangular flat torus [Elektronische Daten] [William Dickinson, Daniel Guillot, Anna Keaton, Sandi Xhumari] 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. Springer Basel AG, 2012 Equal circle packing nationallicence flat torus nationallicence packing graph nationallicence rigidity theory nationallicence Dickinson William Department of Mathematics, Grand Valley State University, 49401, Allendale, MI, USA aut Guillot Daniel Department of Mathematics, Louisiana State University, 70803, Baton Rouge, LA, USA aut Keaton Anna Department of Mathematical Sciences, Clemson University, 29634, Clemson, SC, USA aut Xhumari Sandi Department of Mathematics, University of Connecticut, 06269-3009, Storrs, CT, USA aut Journal of Geometry SP Birkhäuser Verlag Basel 102/1-2(2011-12-01), 27-51 0047-2468 102:1-2<27 2011 102 22 https://doi.org/10.1007/s00022-011-0099-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00022-011-0099-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dickinson William Department of Mathematics, Grand Valley State University, 49401, Allendale, MI, USA aut NATIONALLICENCE 700 1- Guillot Daniel Department of Mathematics, Louisiana State University, 70803, Baton Rouge, LA, USA aut NATIONALLICENCE 700 1- Keaton Anna Department of Mathematical Sciences, Clemson University, 29634, Clemson, SC, USA aut NATIONALLICENCE 700 1- Xhumari Sandi Department of Mathematics, University of Connecticut, 06269-3009, Storrs, CT, USA aut NATIONALLICENCE 773 0- Journal of Geometry SP Birkhäuser Verlag Basel 102/1-2(2011-12-01), 27-51 0047-2468 102:1-2<27 2011 102 22 Metadata rights reserved Springer special CC-BY-NC licence nationallicence SWISSBIB 445813350 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer