Appendix B: Characteristics of the DLP optimal packings presented The following table lists the putative R$_{min}$ ( N ), calculated with accuracy to at least 10 − 6 diameter units, for each packing presented. For comparison with the triangular lattice, alongside each R$_{min}$ ( N ) is listed the smallest radius triangular lattice shell enclosing the centers of at least N disks (not including the central disk). Point group symmetries are additionally listed, as determined also with accuracy to at least 10 − 6 diameter units. DLP optimal packing characteristics Number of disks Figure R$_{min}$ ( N ) Tri. latt. shell Point group 10 6 (top) 1.618034 1.732051 C$_{2}$$_{v}$ 10 6 (center) 1.618034 1.732051 C$_{2}$$_{v}$ 10 6 (bottom) 1.618034 1.732051 D$_{5}$$_{h}$ 11 10 (center) 1.685854 1.732051 C$_{2}$$_{v}$ 15 1 1.873123 2 D$_{5}$$_{h}$ 24 12 (top) 2.425256 2.645751 D$_{3}$$_{h}$ 25 10 (top) 2.497212 2.645751 D$_{5}$$_{h}$ 32 10 (bottom) 2.794164 3 D$_{2}$$_{h}$ 40 13 (top) 3.136712 3.464102 D$_{2}$$_{h}$ 45 12 (center) 3.374023 3.605551 C$_{1}$ 46 15 (bottom) 3.414304 3.605551 C$_{1}$ 59 15 (top) 3.824374 4 C$_{1}$ 60 7 (top) 3.830649 4 C$_{6}$$_{h}$ 66 13 (bottom) 4.104997 4.358899 C$_{1}$ 80 15 (center) 4.514170 4.582576 C$_{1}$ 84 8 (top) 4.581556 4.582576 C$_{i}$ 90 7 (center) 4.783386 5 C$_{6}$$_{h}$ 95 12 (bottom) 4.958096 5.196152 C$_{1}$ 120 8 (center) 5.562401 5.567764 C$_{i}$ 126 7 (bottom) 5.736857 6 C$_{6}$$_{h}$ continued on next page 33