{ "retrieved": "2026-10-25", "rows": { "7": { "cosine": "0.210138312731", "optimal_mark": true, "reference_text": "K. Sch\u00fctte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96\u2013124, doi:10.1007/BF02054944.3\u2062x3\u22129\u2062x2\u22123\u2062x+1", "polynomial": "3*x^3-9*x^2-3*x+1", "sloane_angle": "77.8695421" }, "8": { "cosine": "0.261203874964", "optimal_mark": true, "reference_text": "K. Sch\u00fctte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96\u2013124, doi:10.1007/BF02054944.7\u2062x2+2\u2062x\u22121", "polynomial": "7*x^2+2*x-1", "sloane_angle": "74.8584922" }, "9": { "cosine": "0.333333333334", "optimal_mark": true, "reference_text": "K. Sch\u00fctte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96\u2013124, doi:10.1007/BF02054944.3\u2062x\u22121", "polynomial": "3*x-1", "sloane_angle": "70.5287794" }, "10": { "cosine": "0.404394325217", "optimal_mark": true, "reference_text": "K. Sch\u00fctte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96\u2013124, doi:10.1007/BF02054944; L. Danzer, Finite point-sets on S2 with minimum distance as large as possible, Discrete Math. 60 (1986), 3\u201366, doi:10.1016/0012-365X(86)90002-6.7\u2062x3\u22124\u2062x2\u22122\u2062x+1", "polynomial": "7*x^3-4*x^2-2*x+1", "sloane_angle": "66.1468220" }, "11": { "cosine": "0.447213595500", "optimal_mark": true, "reference_text": "K. Sch\u00fctte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96\u2013124, doi:10.1007/BF02054944; L. Danzer, Finite point-sets on S2 with minimum distance as large as possible, Discrete Math. 60 (1986), 3\u201366, doi:10.1016/0012-365X(86)90002-6.5\u2062x2\u22121", "polynomial": "5*x^2-1", "sloane_angle": "63.4349488" }, "12": { "cosine": "0.447213595500", "optimal_mark": true, "reference_text": "L. Fejes [T\u00f3th], \u00dcber eine Absch\u00e4tzung des k\u00fcrzesten Abstandes zweier Punkte eines auf einer Kugelfl\u00e4che liegenden Punktsystems, Jber. Deutsch. Math.-Verein. 53 (1943), 66\u201368.5\u2062x2\u22121", "polynomial": "5*x^2-1", "sloane_angle": "63.4349488" }, "13": { "cosine": "0.542636486830", "optimal_mark": true, "reference_text": "K. Sch\u00fctte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96\u2013124, doi:10.1007/BF02054944; O. R. Musin and A. S. Tarasov, The strong thirteen spheres problem, Discrete Comput. Geom. 48 (2012), 128\u2013141, doi:10.1007/s00454-011-9392-2.x8\u221224\u2062x7\u221212\u2062x6+8\u2062x5+38\u2062x4+24\u2062x3\u221212\u2062x2\u22128\u2062x+1", "polynomial": "x^8-24*x^7-12*x^6+8*x^5+38*x^4+24*x^3-12*x^2-8*x+1", "sloane_angle": "57.1367031" }, "14": { "cosine": "0.563950300361", "optimal_mark": true, "reference_text": "K. Sch\u00fctte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96\u2013124, doi:10.1007/BF02054944; O. R. Musin and A. S. Tarasov, The Tammes problem for N=14, Exp. Math. 24 (2015), 460\u2013468, doi:10.1080/10586458.2015.1022842.4\u2062x4\u22122\u2062x3+3\u2062x2\u22121", "polynomial": "4*x^4-2*x^3+3*x^2-1", "sloane_angle": "55.6705700" }, "15": { "cosine": "0.592605902926", "optimal_mark": true, "reference_text": "K. Sch\u00fctte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96\u2013124, doi:10.1007/BF02054944; D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158\u2013165, doi:10.1107/S0108767390011370; mt0-svg, The Tammes problem for fifteen points, preprint, 2026, doi:10.5281/zenodo.23450670, https://github.com/mt0-svg/tammes-15.13\u2062x5\u2212x4+6\u2062x3+2\u2062x2\u22123\u2062x\u22121", "polynomial": "13*x^5-x^4+6*x^3+2*x^2-3*x-1", "sloane_angle": "53.6578501" }, "16": { "cosine": "0.612294616483", "optimal_mark": false, "reference_text": "K. Sch\u00fctte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96\u2013124, doi:10.1007/BF02054944.23\u2062x6+6\u2062x5+5\u2062x4+4\u2062x3\u22123\u2062x2\u22122\u2062x\u22121", "polynomial": "23*x^6+6*x^5+5*x^4+4*x^3-3*x^2-2*x-1", "sloane_angle": "52.2443957" }, "17": { "cosine": "0.628094415071", "optimal_mark": false, "reference_text": "L. Danzer, Finite point-sets on S2 with minimum distance as large as possible, Discrete Math. 60 (1986), 3\u201366, doi:10.1016/0012-365X(86)90002-6.4\u2062x10\u221292\u2062x9+24\u2062x8+128\u2062x7\u221258\u2062x6\u221278\u2062x5+35\u2062x4+32\u2062x3\u22124\u2062x2\u22126\u2062x\u22121", "polynomial": "4*x^10-92*x^9+24*x^8+128*x^7-58*x^6-78*x^5+35*x^4+32*x^3-4*x^2-6*x-1", "sloane_angle": "51.0903285" }, "18": { "cosine": "0.648695832224", "optimal_mark": false, "reference_text": "T. Tarnai and Zs. G\u00e1sp\u00e1r, Improved packing of equal circles on a sphere and rigidity of its graph, Math. Proc. Cambridge Philos. Soc. 93 (1983), 191\u2013218, doi:10.1017/S0305004100060485.216\u2062x11+108\u2062x10+118\u2062x9+209\u2062x8\u2212100\u2062x7\u2212160\u2062x6+40\u2062x5+46\u2062x4\u221220\u2062x3\u221212\u2062x2+2\u2062x+1", "polynomial": "216*x^11+108*x^10+118*x^9+209*x^8-100*x^7-160*x^6+40*x^5+46*x^4-20*x^3-12*x^2+2*x+1", "sloane_angle": "49.5566548" }, "19": { "cosine": "0.673116887561", "optimal_mark": false, "reference_text": "D. E. Lazi\u0107, V. \u0160enk, and I. \u0160e\u0161kar, Arrangements of points on a sphere which maximize the least distance, Bull. Appl. Math. 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L. van der Waerden, Punkte auf der Kugel. Drei Zus\u00e4tze, Math. Ann. 125 (1952), 213\u2013222, doi:10.1007/BF01343118.21\u2062x3\u22129\u2062x2\u22125\u2062x+1", "polynomial": "21*x^3-9*x^2-5*x+1", "sloane_angle": "47.4310362" }, "21": { "cosine": "0.699498431067", "optimal_mark": false, "reference_text": "D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158\u2013165, doi:10.1107/S0108767390011370.", "sloane_angle": "45.6132231" }, "22": { "cosine": "0.710306258580", "optimal_mark": false, "reference_text": "D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158\u2013165, doi:10.1107/S0108767390011370.Minimal polynomial listed in plain text data", "polynomial": "486*x^18+13113*x^17+114996*x^16+117476*x^15+658256*x^14+378752*x^13-347056*x^12-121388*x^11+81724*x^10-70886*x^9-55992*x^8+12716*x^7+6528*x^6-2392*x^5-208*x^4+284*x^3+14*x^2+5*x+4", "sloane_angle": "44.7401612" }, "23": { "cosine": "0.722846984869", "optimal_mark": false, "reference_text": "T. Tarnai and Zs. G\u00e1sp\u00e1r, Arrangement of 23 points on a sphere (on a conjecture of R. M. Robinson), Proc. Roy. Soc. London Ser. A 433 (1991), 257\u2013267, doi:10.1098/rspa.1991.0046.", "sloane_angle": "43.7099642" }, "24": { "cosine": "0.723078468334", "optimal_mark": true, "reference_text": "R. M. Robinson, Arrangements of 24 points on a sphere, Math. Ann. 144 (1961), 17\u201348, doi:10.1007/BF01396539.7\u2062x3+x2\u22123\u2062x\u22121", "polynomial": "7*x^3+x^2-3*x-1", "sloane_angle": "43.6907671" }, "25": { "cosine": "0.747398628578", "optimal_mark": false, "reference_text": "D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. 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A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. 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Tarnai and Zs. G\u00e1sp\u00e1r, Improved packing of equal circles on a sphere and rigidity of its graph, Math. Proc. Cambridge Philos. Soc. 93 (1983), 191\u2013218, doi:10.1017/S0305004100060485.Minimal polynomial listed in plain text data", "polynomial": "16*x^24-128*x^23+536*x^22-2088*x^21+4977*x^20-12258*x^19+20672*x^18-36126*x^17+51043*x^16-73408*x^15+104128*x^14-137928*x^13+175090*x^12-181700*x^11+155936*x^10-92916*x^9+32222*x^8+6608*x^7-16568*x^6+8192*x^5-1843*x^4-490*x^3+128*x^2+2*x-1", "sloane_angle": "40.6776007" }, "28": { "cosine": "0.773230262338", "optimal_mark": false, "reference_text": "D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158\u2013165, doi:10.1107/S0108767390011370.", "sloane_angle": "39.3551436" }, "29": { "cosine": "0.780281415949", "optimal_mark": false, "reference_text": "D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158\u2013165, doi:10.1107/S0108767390011370.", "sloane_angle": "38.7136512" }, "30": { "cosine": "0.781551875095", "optimal_mark": false, "reference_text": "B. W. Clare and D. L. Kepert, The closest packing of equal circles on a sphere, Proc. Roy. Soc. London Ser. A 405 (1986), 329\u2013344, doi:10.1098/rspa.1986.0056.Minimal polynomial listed in plain text data", "polynomial": "21508124014*x^29+32054106929*x^28-17306462662*x^27-25038151480*x^26+45587477052*x^25+38755887413*x^24-43255133604*x^23-45501640088*x^22+10460524458*x^21+17929512405*x^20-4828786226*x^19-5447284224*x^18+4496890016*x^17+4235161545*x^16-436447576*x^15-1539874224*x^14-487336414*x^13+100621747*x^12+97938998*x^11+20609352*x^10+665516*x^9+320703*x^8+272188*x^7-6712*x^6-34298*x^5-7289*x^4+386*x^3+368*x^2+56*x+3", "sloane_angle": "38.5971159" }, "31": { "cosine": "0.791118613299", "optimal_mark": false, "reference_text": "J. Strohmajer, \u00dcber die Verteilung von Punkten auf der Kugel, Ann. Univ. Sci. Budapest. E\u00f6tv\u00f6s Sect. Math. 6 (1963), 49\u201353.Minimal polynomial listed in plain text data", "polynomial": "762939453125*x^66-7749023437500000*x^65-549435976806640625*x^64-11954964334375000000*x^63+46354290204062500000*x^62+296025528806187500000*x^61+490694826896712500000*x^60-2924709240882350000000*x^59-6800355886385641875000*x^58-366339002678087500000*x^57+24369506192176385375000*x^56+27001547365967091000000*x^55-21809158347127162000000*x^54-57924024899601366500000*x^53+216864844649587000000*x^52+85459665184041748000000*x^51+54781050077892013637500*x^50-58750644174610964300000*x^49-82881366173951176087500*x^48+10813834042651693800000*x^47+68671909889015111100000*x^46+21880288415145669500000*x^45-33835279909942372260000*x^44-28742278663291060560000*x^43+5059474474277195855000*x^42+18072340935967350180000*x^41+5081122618349672485000*x^40-7348044648411661000000*x^39-4855343931749555912000*x^38+1756201950891108268000*x^37+2191537623864678896000*x^36-149574226224283200000*x^35-601704498228424443250*x^34-31377517351471092000*x^33+105699566552688975850*x^32+7583888617243473600*x^31-11670500395907146400*x^30+897723129303914400*x^29+727136477631583200*x^28-648477435737936000*x^27-15984936748662600*x^26+140013663478850400*x^25-729722733211800*x^24-18513532467761600*x^23+83825458355200*x^22+1742577366650400*x^21-11081142856000*x^20-124659358585600*x^19+1556588076380*x^18+7006344894560*x^17-185033832620*x^16-323267164480*x^15+18407781280*x^14+13515780640*x^13-1414879840*x^12-552613760*x^11+81291880*x^10+19660000*x^9-3587720*x^8-472000*x^7+128960*x^6+5280*x^5-3840*x^4+85*x^2-1", "sloane_angle": "37.7098291" }, "32": { "cosine": "0.793616614872", "optimal_mark": false, "reference_text": "L. Danzer, Finite point-sets on S2 with minimum distance as large as possible, Discrete Math. 60 (1986), 3\u201366, doi:10.1016/0012-365X(86)90002-6.Minimal polynomial listed in plain text data", "polynomial": "6561*x^22-4374*x^21-94041*x^20+1289844*x^19+3605067*x^18-4301046*x^17+6019389*x^16+238896*x^15-10407366*x^14+7894164*x^13+7975830*x^12-7790088*x^11-3481466*x^10+3831332*x^9+843658*x^8-1303376*x^7-311819*x^6+148290*x^5+39667*x^4-3660*x^3-1185*x^2+18*x+9", "sloane_angle": "37.4752140" }, "33": { "cosine": "0.806397613648", "optimal_mark": false, "reference_text": "D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158\u2013165, doi:10.1107/S0108767390011370.", "sloane_angle": "36.2545530" }, "34": { "cosine": "0.810984337204", "optimal_mark": false, "reference_text": "D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158\u2013165, doi:10.1107/S0108767390011370.", "sloane_angle": "35.8077844" }, "35": { "cosine": "0.815937771500", "optimal_mark": false, "reference_text": "N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994\u20131996.", "sloane_angle": "35.3198076" }, "36": { "cosine": "0.817248185290", "optimal_mark": false, "reference_text": "D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158\u2013165, doi:10.1107/S0108767390011370.", "sloane_angle": "35.1897322" }, "37": { "cosine": "0.824892480240", "optimal_mark": false, "reference_text": "D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158\u2013165, doi:10.1107/S0108767390011370.", "sloane_angle": "34.4224080" }, "38": { "cosine": "0.826583259422", "optimal_mark": false, "reference_text": "E. Sz\u00e9kely, Sur le probl\u00e8me de Tammes, Annales Universitatis Scientiarum Budapestinensis de Rolando E\u00f6tv\u00f6s Nominatae 17 (1974), 157\u2013175, http://annalesm.elte.hu/annales17-1974/Annales_1974_T-XVII.pdf.363\u2062x14+7685\u2062x12+34299\u2062x10\u221277139\u2062x8+68985\u2062x6\u221231833\u2062x4+6561\u2062x2\u2212729", "polynomial": "363*x^14+7685*x^12+34299*x^10-77139*x^8+68985*x^6-31833*x^4+6561*x^2-729", "sloane_angle": "34.2506607" }, "39": { "cosine": "0.833991322411", "optimal_mark": false, "reference_text": "D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158\u2013165, doi:10.1107/S0108767390011370.", "sloane_angle": "33.4890466" }, "40": { "cosine": "0.837162072474", "optimal_mark": false, "reference_text": "B. W. Clare and D. L. Kepert, The closest packing of equal circles on a sphere, Proc. Roy. Soc. London Ser. A 405 (1986), 329\u2013344, doi:10.1098/rspa.1986.0056.", "sloane_angle": "33.1583563" }, "41": { "cosine": "0.841236343029", "optimal_mark": false, "reference_text": "D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158\u2013165, doi:10.1107/S0108767390011370.", "sloane_angle": "32.7290944" }, "42": { "cosine": "0.843331551639", "optimal_mark": false, "reference_text": "E. Sz\u00e9kely, Sur le probl\u00e8me de Tammes, Annales Universitatis Scientiarum Budapestinensis de Rolando E\u00f6tv\u00f6s Nominatae 17 (1974), 157\u2013175, http://annalesm.elte.hu/annales17-1974/Annales_1974_T-XVII.pdf.Minimal polynomial listed in plain text data", "polynomial": "48828125*x^58+390625000*x^57+12373046875*x^56+33828125000*x^55+1080183593750*x^54-1412140625000*x^53+86275913281250*x^52+41120596875000*x^51+895022314921875*x^50-1096208251250000*x^49+7523766956078125*x^48-3202274778250000*x^47+38560617034787500*x^46-45908490400150000*x^45+164851664304702500*x^44-138028786623310000*x^43+425541539614768125*x^42-639540976580725000*x^41+1138013289613876875*x^40-980709576561345000*x^39+641612839908020250*x^38-1099840764722579000*x^37+1026059830310012750*x^36-196989489978399000*x^35+654982947945770875*x^34-754795472614732000*x^33-398523767152254475*x^32+654480411632778400*x^31+10454259123593000*x^30-345869580675972000*x^29+64152661630902200*x^28+115637587011653600*x^27-38486739494235265*x^26-27682878412927400*x^25+14423812229565385*x^24+5614638421553400*x^23-3841692135094550*x^22-1033229977805400*x^21+810524051136094*x^20+192226833055048*x^19-142323372063487*x^18-39299134379216*x^17+20150391962975*x^16+8764135432048*x^15-833633514388*x^14-899445607280*x^13-54047766300*x^12+44816358352*x^11+6089927719*x^10-1206931768*x^9-236426287*x^8+18134696*x^7+4888486*x^6-143880*x^5-57678*x^4+472*x^3+369*x^2-1", "sloane_angle": "32.5063863" }, "43": { "cosine": "0.847208865437", "optimal_mark": false, "reference_text": "N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994\u20131996.", "sloane_angle": "32.0906244" }, "44": { "cosine": "0.848201378305", "optimal_mark": false, "reference_text": "D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158\u2013165, doi:10.1107/S0108767390011370.", "sloane_angle": "31.9834230" }, "45": { "cosine": "0.854249474082", "optimal_mark": false, "reference_text": "D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158\u2013165, doi:10.1107/S0108767390011370.", "sloane_angle": "31.3230814" }, "46": { "cosine": "0.857534166865", "optimal_mark": false, "reference_text": "D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158\u2013165, doi:10.1107/S0108767390011370.", "sloane_angle": "30.9591635" }, "47": { "cosine": "0.859122361410", "optimal_mark": false, "reference_text": "D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158\u2013165, doi:10.1107/S0108767390011370.", "sloane_angle": "30.7818159" }, "48": { "cosine": "0.859292295076", "optimal_mark": false, "reference_text": "R. M. Robinson, Finite sets of points on a sphere with each nearest to five others, Math. Ann. 179 (1969), 296\u2013318, doi:10.1007/BF01350775.34\u2062x5+15\u2062x4\u221212\u2062x3\u221214\u2062x2\u22126\u2062x\u22121", "polynomial": "34*x^5+15*x^4-12*x^3-14*x^2-6*x-1", "sloane_angle": "30.7627855" }, "49": { "cosine": "0.866691479049", "optimal_mark": false, "reference_text": "D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158\u2013165, doi:10.1107/S0108767390011370.", "sloane_angle": "29.9235851" }, "50": { "cosine": "0.868173209127", "optimal_mark": false, "reference_text": "E. Sz\u00e9kely, Sur le probl\u00e8me de Tammes, Annales Universitatis Scientiarum Budapestinensis de Rolando E\u00f6tv\u00f6s Nominatae 17 (1974), 157\u2013175, http://annalesm.elte.hu/annales17-1974/Annales_1974_T-XVII.pdf.Minimal polynomial listed in plain text data", "polynomial": "386*x^12+1679*x^11+6433*x^10-743*x^9-2287*x^8-19290*x^7+8490*x^6+19170*x^5-5580*x^4-6885*x^3-1755*x^2+2997*x-567", "sloane_angle": "29.7529564" }, "51": { "cosine": "0.871484364931", "optimal_mark": false, "reference_text": "N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994\u20131996.", "sloane_angle": "29.3684069" }, "52": { "cosine": "0.872966708781", "optimal_mark": false, "reference_text": "D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158\u2013165, doi:10.1107/S0108767390011370.Minimal polynomial listed in plain text data", "polynomial": "448001*x^16+1243448*x^15+2260200*x^14+2517944*x^13+1365340*x^12-424904*x^11-1782664*x^10-1847944*x^9-864186*x^8-12568*x^7+192280*x^6+95976*x^5+19676*x^4+936*x^3-248*x^2-24*x+1", "sloane_angle": "29.1947579" }, "53": { "cosine": "0.876189803956", "optimal_mark": false, "reference_text": "D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158\u2013165, doi:10.1107/S0108767390011370.", "sloane_angle": "28.8138972" }, "54": { "cosine": "0.877004306358", "optimal_mark": false, "reference_text": "D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158\u2013165, doi:10.1107/S0108767390011370.", "sloane_angle": "28.7169205" }, "55": { "cosine": "0.880785046525", "optimal_mark": false, "reference_text": "D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. 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