# Last edited on 2012-01-23 04:17:22 by stolfilocal COMPUTED OPTIMUM CONFIGURATIONS Some computed optimum configurations for the Rutherford atom with cloud of uniform density: 001:1:0 0.000 center 002:1:0 1.890 symmetric 003:2:0 5.670 triangle 003:2:1 6.325 three in line 003:2:2 5.670 triangle 004:3:0 11.339 tetrahedron 004:3:2 11.339 tetrahedron 005:3:0 19.196 3-bipyramid 005:3:1 20.225 square + center 005:3:3 19.959 tetrahedron + center 006:3:0 28.936 octahedron 006:3:1 28.936 octahedron 006:3:2 28.936 octahedron 007:3:0 41.031 5-bipyramid, slightly distorted 007:3:1 41.687 octahedron + center 007:3:3 41.687 octahedron + center 008:3:0 55.095 4-antiprism 008:3:1 55.593 6-bipyramid 008:3:2 55.217 hexahedron 009:3:0 71.322 3-bisantiprism (3-prism with 4-pyramids on sides) 009:3:1 72.049 hexahedron + center 009:3:3 72.049 hexahedron + center 010:3:0 89.737 irregular, 1 shell 010:3:1 90.219 hexahedron + top/botom 4-pyramids, squashed and slightly distorted 011:3:0 110.415 irregular, 1 shell 011:3:1 111.072 hexahedron + top/botom 4-pyramids + center, distorted 012:3:0 133.363 irregular, 1 shell + center 012:3:1 132.942 icosahedron 012:3:2 132.943 icosahedron 013:3:0 158.092 irregular, 1 shell + 2 inside 013:3:1 157.955 icosahedron + center, distorted 013:3:3 157.936 icosahedron + center 014:3:0 185.813 icosahedron + 2 inside, distorted 014:3:1 185.289 hexahedron + octahedron 015:3:0 214.307 6-prism + top/botom 6-pyramids + center, distorted 015:3:1 214.375 6-prism + top/botom 6-pyramids + center, slightly distorted 016:3:0 245.732 irregular, 1 shell + center (some regularity?) 016:3:1 246.464 6-prism + top/botom 6-pyramids + 2 inside, slightly distorted 017:3:0 279.338 irregular, 1 shell + center 017:3:1 279.812 irregular, 1 shell + center 018:3:0 315.137 irregular, 1 shell + center 018:3:1 316.105 irregular, 1 shell + 2 inside 019:3:0 353.315 irregular, 1 shell + center 019:3:1 353.610 5-8-5-tower + center (some regularity?) 020:3:0 394.143 irregular (2 shells?) 020:3:1 394.009 irregular (2 shells?) 020:3:2 396.247 dodecahedron 021:3:0 436.435 irregular, 1 shell + 2 inside 021:3:1 435.874 1-5-8-5-1-tower + center, slightly distorted 021:3:3 437.387 dodecahedron + center 022:3:0 481.044 irregular, 1 shell + 2 inside 022:3:1 480.667 irregular, 1 shell + 2 inside (some regularity?) 023:3:0 527.666 irregular, 1 shell + 2 inside 023:3:1 527.510 1-6-8-6-1-tower + center 024:3:0 576.742 very irregular, 1 shell + 2 inside 024:3:1 576.486 4-7-7-4-tower + 2 inside, distorted 031:3:0 990.278 very irregular, 1 shell + 8 inside + 1 outside cloud! 031:3:1 983.560 irregular, 1 shell + center + 4 inside 030:3:0 918.485 irregular, 1 shell + 5 inside in irregular positions 030:3:1 918.734 irregular, 1 shell + 6 inside in irregular paired positions (some regularity?) 032:3:0 1050.126 irregular, 1 shell + 7 inside in irregular positions 032:3:1 1049.678 irregular, 1 shell + 6 inside in irregular paired positions (some regularity?) 033:3:0 1118.172 irregular?, 1 shell + 5 inside 033:3:1 1119.234 dodecahedron + rectangle inside + center + 8 5-pyramids on faces, slightly distorted [1] 036:3:0 1338.191 irregular?, 1 shell + 6 inside 036:3:1 1338.015 irregular?, 1 shell + 6 inside 060:3:0 3826.735 irregular, 1 shell + ~18 inside in irregular positions (some regularity?) 060:3:1 3822.082 1 outer irregular shell of 44 + 1 inner shell of 14 (regular?) + 2 near center Configuration [1] is a dodecahedron + center + 12 5-pyramids on all faces, except that 4 of those pyramids are pushed inwards instead of outwards, with their tips creating a rectangle inside the dodecahedron. The configuration has the symmetry of a parallelepiped with unequal sides. EVOLUTION OF MIN POTENTIAL Data to plot: 1 0.000 center 2 1.890 symmetric 3 5.670 triangle 4 11.339 tetrahedron 5 19.196 3-bipyramid 6 28.936 octahedron 7 41.031 5-bipyramid, slightly distorted 8 55.095 4-antiprism 9 71.322 3-bisantiprism (3-prism with 4-pyramids on sides) 10 89.737 irregular, 1 shell 11 110.415 irregular, 1 shell 12 132.943 icosahedron 13 157.936 icosahedron + center 14 185.289 hexahedron + octahedron 15 214.307 6-prism + top/botom 6-pyramids + center, distorted 16 245.732 irregular, 1 shell + center (some regularity?) 17 279.338 irregular, 1 shell + center 18 315.137 irregular, 1 shell + center 19 353.315 irregular, 1 shell + center 20 394.009 irregular (2 shells?) 21 435.874 1-5-8-5-1-tower + center, slightly distorted 22 480.667 irregular, 1 shell + 2 inside (some regularity?) 23 527.510 1-6-8-6-1-tower + center 24 576.486 4-7-7-4-tower + 2 inside, distorted 30 918.485 irregular, 1 shell + 5 inside in irregular positions 31 983.560 irregular, 1 shell + center + 4 inside 32 1049.678 irregular, 1 shell + 6 inside in irregular paired positions (some regularity?) 33 1118.172 irregular?, 1 shell + 5 inside 36 1338.015 irregular?, 1 shell + 6 inside 60 3822.082 1 outer irregular shell of 44 + 1 inner shell of 14 (regular?) + 2 near center Asymptotic model: minpot(nq) = 1.08*(nq - 0.70)**2 This model is extremely accurate from {nq=1} to {nq=60}.