# This file contains summary data from " Knot Tightening By Constrained Gradient Descent " by Ashton, Cantarella, Piatek, Rawdon. # and " The Shapes of Tight Composite Knots " by Cantarella, La Pointe, Rawdon. # Knot type Polygonal Ropelength Ropelength Bound Edges Residual Writhe 2_2_1_#_5_1_m 63.8111 63.7957 515 0.0074089 8.284290 2_2_1_#_2_2_1_#_3_1_TreeB 65.9282 65.9152 531 0.0119118 0.596441 2_2_1_#_5_2_m 64.6418 64.6267 521 0.000979944 6.586032 2_2_1_#_5_1 63.8109 63.7959 515 0.00744771 -4.284305 2_2_1_#_4_2_1 56.6193 56.6063 457 0.00749432 -1.153986 2_2_1_#_4_1 57.4815 57.4716 464 0.000899649 1.982431 2_2_1 25.1415 25.1334 202 3.85112e-05 nan 2_2_1_#_5_2_1_TreeA 65.3130 65.3008 527 0.000748949 3.386358 2_2_1_#_2_2_1_TreeA 41.7045 41.7009 536 0.0085687 4.000322 2_2_1_#_2_2_1_#_3_1_TreeA 63.9294 63.9162 516 0.002337 0.580844 2_2_1_#_5_2 64.6418 64.6267 521 0.000979944 -2.586032 2_2_1_#_5_2_1_m 65.3118 65.2989 550 0.000747302 0.613996 2_2_1_#_3_1 49.3368 49.3280 451 0.000748372 -1.413447 3_1_#_9_12 103.6976 103.6739 842 0.0025852 -7.994630 3_1_#_8_19_m 83.3883 83.3718 683 0.00177235 5.271581 3_1_m_#_3_1_m 57.0564 57.0406 457 0.00749582 6.811189 3_1_#_8_15 96.5430 96.5195 775 0.00263797 -11.418072 3_1_m_#_8_19_m 83.6832 83.6685 671 0.00558381 12.257860 3_1_m_#_9_20 103.4146 103.3938 828 0.00879101 9.651710 3_1_m_#_9_15 103.5576 103.5382 833 0.00256231 -1.120075 3_1_#_9_2_m 101.1980 101.1733 814 0.00209839 3.407030 3_1_m_#_5_1 71.5920 71.5782 573 0.0026267 -2.867483 3_1_#_9_8 102.8037 102.7785 825 0.00749906 -5.715897 3_1_m_#_8_15 96.3309 96.3086 773 0.000749728 -4.585362 3_1_#_3_1_m_#_6_2 103.4807 103.4581 833 0.000749816 -2.833042 3_1_#_9_39 104.5315 104.5099 837 0.000879027 -8.002594 3_1_m_#_3_1_m_#_6_3 103.6868 103.6657 851 0.00749925 6.848794 3_1_m_#_7_2 88.2406 88.2208 707 0.0010176 9.103011 3_1_m_#_9_33_rm 105.7663 105.7415 850 0.00749815 3.945693 3_1_#_6_1 81.0975 81.0871 651 0.00437729 -4.547552 3_1_#_8_19 83.6832 83.6685 671 0.00558381 -12.257860 3_1_#_9_33_rm 104.8542 104.8320 843 0.00461765 -2.791785 3_1_m_#_9_38 104.7605 104.7395 840 0.00106907 -5.176495 3_1_m_#_9_40_m 105.9079 105.8912 852 0.00748159 6.834091 3_1_#_9_45_m 97.7069 97.6875 784 0.00414596 1.711328 3_1_m_#_4_1_#_5_1_m 102.4202 102.3979 822 0.00569643 9.667281 3_1_#_8_9 96.4648 96.4465 789 0.00726236 -3.380828 3_1_m_#_8_1 94.0559 94.0357 755 0.00273898 1.156062 3_1_#_9_3_m 101.2733 101.2530 814 0.00294139 6.906372 3_1_m_#_3_1_m_#_3_1_m_#_3_1_m 101.6027 101.5762 814 0.000749837 13.703391 3_1_m_#_8_20 85.9539 85.9362 689 0.00205972 1.517749 3_1_#_9_4_m 101.3631 101.3396 812 0.000744073 5.145652 3_1_#_7_7_m 88.7656 88.7463 714 0.00270317 -2.827387 3_1_m_#_3_1_m_#_6_2_m 102.6044 102.5834 830 0.000749917 9.661364 3_1_#_3_1_m 57.0860 57.0726 457 0.00269831 0.000498 3_1_m_#_7_6 88.4548 88.4328 711 0.00074999 -0.027220 3_1_m_#_5_2_m 72.4320 72.4124 580 0.000979741 7.978272 3_1_m_#_9_27 104.4665 104.4433 840 0.00749932 2.842489 3_1_#_9_21 103.8251 103.8066 835 0.00749624 -7.960527 3_1_#_8_4 94.6319 94.6112 762 0.000748228 -5.092871 3_1_m_#_8_18 98.1916 98.1710 802 0.000749464 3.323461 3_1_#_9_48 97.1271 97.1086 778 0.00402116 -7.387061 3_1_m_#_9_44 94.0951 94.0758 756 0.00749674 2.095921 3_1_#_9_7 103.2779 103.2555 828 0.0755771 -11.969983 3_1_#_3_1_m_#_5_2_m 95.0572 95.0378 762 0.00749595 4.560072 3_1_#_3_1_#_6_1_m 103.3027 103.2804 828 0.000979998 -5.700541 3_1_#_9_43 93.7030 93.6860 753 0.00824332 -8.913497 3_1_#_8_11_m 95.6444 95.6245 767 0.00749901 -7.411717 3_1_#_9_43_m 93.8072 93.7849 766 0.000746229 2.026869 3_1_m_#_9_6_m 102.4780 102.4520 824 0.00342591 13.730968 3_1_m_#_9_48_m 97.1271 97.1086 778 0.00402116 7.387061 3_1_#_3_1_#_3_1_m 79.5760 79.5577 640 0.00741396 -3.397163 3_1_#_8_3 95.5053 95.4842 766 0.00420584 -3.394078 3_1_#_9_11_m 102.8090 102.7847 827 0.000749769 2.913649 3_1_#_9_42_m 91.7888 91.7713 736 0.00292783 -2.196995 3_1_#_9_40_m 105.7624 105.7399 850 0.00258468 0.024142 3_1_m_#_9_34 105.6153 105.5960 849 0.00362192 2.776189 3_1_#_9_9 102.6543 102.6279 824 0.000979976 -13.682039 3_1_#_8_11 95.6990 95.6792 768 0.00074996 0.609193 3_1_#_9_33_m 104.8542 104.8320 843 0.00461765 -2.791785 3_1_#_8_15_m 96.3309 96.3086 773 0.000749728 4.585362 3_1_#_9_47_m 97.1694 97.1525 781 0.00074996 -0.674091 3_1_#_8_6_m 95.6406 95.6194 769 0.00074981 0.614897 3_1_#_9_19 103.5730 103.5498 833 0.000749753 -3.954406 3_1_m_#_9_18_m 103.7734 103.7515 834 0.00749878 11.984756 3_1_m_#_9_5_m 102.6047 102.5830 826 0.00074981 10.284563 3_1_m_#_9_3 101.2733 101.2530 814 0.00294139 -6.906372 3_1_#_3_1_m_#_6_1 102.2648 102.2426 822 0.00747444 -1.133477 3_1_#_9_23_m 104.2024 104.1771 838 0.000749051 5.198591 3_1_m_#_9_32_rm 104.6427 104.6170 841 0.00749604 6.822216 3_1_#_8_8 96.3972 96.3752 773 0.00749955 -4.560749 3_1_m_#_9_26 104.2070 104.1829 838 0.000749843 -0.030490 3_1_#_8_21 87.8130 87.7930 703 0.000749661 -8.081426 3_1_#_9_20 103.6733 103.6491 836 0.00748839 2.894656 3_1_#_8_20_m 85.9539 85.9362 689 0.00205972 -1.517749 3_1_m_#_8_9 96.4648 96.4465 789 0.00726236 3.380828 3_1_#_9_42 92.0154 91.9999 753 0.0074864 -4.712804 3_1_#_8_10_m 96.6540 96.6326 778 0.00749976 -0.583381 3_1_#_5_2_m 72.5511 72.5342 581 0.000749012 1.183369 3_1_#_5_1 71.5596 71.5434 573 0.00298312 -9.672253 3_1_m_#_8_16_m 96.5134 96.4968 774 0.000747715 6.219762 3_1_m_#_7_4_m 87.8528 87.8415 884 0.00846685 9.145940 3_1_#_8_16 96.5134 96.4968 774 0.000747715 -6.219762 3_1_#_9_16 103.3191 103.2939 838 0.00614573 -13.658427 3_1_m_#_9_32_r 104.5979 104.5787 838 0.00103131 -0.022319 3_1_#_3_1_#_5_2 94.8079 94.7929 760 0.00300342 -11.419576 3_1_#_9_8_m 103.0043 102.9798 828 0.00243824 -1.101374 3_1_m_#_9_10 103.0489 103.0286 829 0.000748655 -5.182208 3_1_#_8_1_m 94.0559 94.0357 755 0.00273898 -1.156062 3_1_m_#_8_2 94.6812 94.6596 761 0.00748055 -2.316416 3_1_m_#_7_5 88.0931 88.0705 708 0.000748343 -3.982827 3_1_#_9_29 104.1302 104.1072 838 0.00323791 -5.629837 3_1_#_9_17_m 103.6475 103.6233 833 0.00749868 -1.175944 3_1_m_#_8_12 96.4812 96.4653 773 0.00435906 3.438958 3_1_#_9_26 104.2767 104.2517 838 0.00242971 -6.821012 3_1_m_#_9_9_m 102.6543 102.6279 824 0.000979976 13.682039 3_1_m_#_9_17 103.6475 103.6233 833 0.00749868 1.175944 3_1_#_9_32 104.6427 104.6170 841 0.00749604 -6.822216 3_1_m_#_9_49_m 96.2858 96.2688 771 0.00209222 11.398099 3_1_#_6_2_m 80.4299 80.4144 647 0.0021862 -0.563844 3_1_#_3_1_#_6_2 102.6044 102.5834 830 0.000749917 -9.661364 3_1_#_9_15 103.6065 103.5819 833 0.000749854 -7.925611 3_1_#_7_6_m 88.4548 88.4328 711 0.00074999 0.027220 3_1_#_8_7_m 95.6184 95.5937 766 0.000979637 -0.539426 3_1_m_#_7_4 87.4828 87.4585 701 0.00749877 -2.354117 3_1_m_#_9_29 104.9645 104.9426 844 0.00170585 1.192767 3_1_m_#_6_1 79.7343 79.7192 642 0.00111086 2.251082 3_1_m_#_8_1_m 93.9165 93.8997 753 0.00748111 5.664189 3_1_#_5_2 72.4320 72.4124 580 0.000979741 -7.978272 3_1_m_#_5_1_m 71.5596 71.5434 573 0.00298312 9.672253 3_1_#_8_2_m 94.6812 94.6596 761 0.00748055 2.316416 3_1_#_8_12 96.4812 96.4653 773 0.00435906 -3.438958 3_1_#_9_1 99.8708 99.8489 803 0.00266069 -15.447318 3_1_m_#_7_6_m 88.5653 88.5482 721 0.00288905 6.829571 3_1_m_#_4_1_#_5_2_m 106.1991 106.1759 853 0.00749969 7.997864 3_1_m_#_9_2_m 101.0978 101.0758 813 0.007495 10.216943 3_1_#_9_44 93.8583 93.8392 753 0.00718718 -4.764646 3_1_m_#_8_21_m 87.8130 87.7930 703 0.000749661 8.081426 3_1_#_8_17_r 97.4373 97.4130 784 0.000749996 -3.398243 3_1_#_8_16_m 96.8380 96.8177 778 0.000747438 -0.576189 3_1_m_#_9_22 104.1172 104.0939 837 0.00749851 1.122581 3_1_m_#_8_7 95.6184 95.5937 766 0.000979637 0.539426 3_1_#_9_15_m 103.5576 103.5382 833 0.00256231 1.120075 3_1_m_#_9_9 102.7778 102.7507 824 0.00749344 -6.839370 3_1_#_9_49_m 96.1726 96.1560 771 0.000979922 4.543013 3_1_m_#_8_21 88.0119 87.9904 705 0.000749862 -1.234572 3_1_m_#_8_20_m 85.5508 85.5323 687 0.000979938 5.349299 3_1_#_4_1_#_5_1 102.4202 102.3979 822 0.00569643 -9.667281 3_1_#_8_2 94.4211 94.3999 760 0.00961308 -9.106061 3_1_m_#_9_46 91.3309 91.3096 732 0.00749857 0.871546 3_1_#_3_1_m_#_3_1_m 79.5760 79.5577 640 0.00741396 3.397163 3_1_#_9_23 104.5867 104.5611 841 0.00749795 -11.987275 3_1_m_#_8_17 97.4373 97.4130 784 0.000749996 3.398243 3_1_m_#_8_11 95.6444 95.6245 767 0.00749901 7.411717 3_1_#_6_3 81.0233 81.0038 651 0.00074937 -3.419522 3_1_#_8_17 97.4373 97.4130 784 0.000749996 -3.398243 3_1_#_9_5 102.6047 102.5830 826 0.00074981 -10.284563 3_1_#_9_37_m 103.7506 103.7260 834 0.00136325 -2.820111 3_1_m_#_9_32 104.5979 104.5787 838 0.00103131 -0.022319 3_1_m_#_6_2_m 80.2461 80.2432 1285 0.00750123 6.220529 3_1_m_#_9_29_m 104.1302 104.1072 838 0.00323791 5.629837 3_1_#_3_1_#_6_1 102.0861 102.0616 818 0.0202972 -7.982248 3_1_#_7_1_m 85.8183 85.7996 689 0.00228588 5.751521 3_1_m_#_9_41_m 104.6749 104.6535 852 0.000749962 5.149623 3_1_m_#_9_18 103.8268 103.8019 832 0.00218772 -5.221478 3_1_#_9_18_m 103.8268 103.8019 832 0.00218772 5.221478 3_1_m_#_9_49 96.1726 96.1560 771 0.000979922 -4.543013 3_1_m_#_3_1_m_#_6_2 103.4974 103.4697 834 0.00749219 4.013726 3_1_#_3_1_#_5_1 93.7909 93.7665 751 0.000979983 -13.115269 3_1_#_3_1_m_#_5_1_m 94.0847 94.0626 756 0.0074947 6.256318 3_1_#_9_28 104.2529 104.2284 838 0.00749595 -6.842945 3_1_m_#_9_10_m 102.8166 102.7923 827 0.00409367 12.012121 3_1_m_#_9_3_m 101.2324 101.2087 815 0.00074802 13.720535 3_1_m_#_9_21 103.8422 103.8195 846 0.00584692 -1.196834 3_1_m_#_9_39_m 104.5315 104.5099 837 0.000879027 8.002594 3_1_m_#_9_39 104.8488 104.8266 843 0.00749833 -1.148222 3_1_m_#_9_47 97.1694 97.1525 781 0.00074996 0.674091 3_1_m_#_9_35_m 102.4450 102.4200 823 0.0216144 -3.504218 3_1_#_9_22_m 104.1172 104.0939 837 0.00749851 -1.122581 3_1_#_8_14 97.1937 97.1716 782 0.0074987 -7.350732 3_1 32.7437 32.7436 2400 0.00622201 -3.416633 3_1_m_#_9_37_m 103.5436 103.5226 833 0.00662157 3.942460 3_1_#_3_1_#_6_3 103.6868 103.6657 851 0.00749925 -6.848794 3_1_m_#_9_33_r 104.8542 104.8320 843 0.00461765 2.791785 3_1_#_8_14_m 97.0261 97.0000 780 0.000749617 0.555564 3_1_m_#_9_2 101.1980 101.1733 814 0.00209839 -3.407030 3_1_m_#_8_13_m 96.4375 96.4168 776 0.00749606 4.587372 3_1_m_#_3_1_m_#_6_1_m 102.0861 102.0616 818 0.0202972 7.982248 3_1_#_8_21_m 88.0119 87.9904 705 0.000749862 1.234572 3_1_#_9_22 103.9690 103.9438 835 0.000749429 -5.648028 3_1_m_#_9_28_m 104.2529 104.2284 838 0.00749595 6.842945 3_1_m_#_9_8_m 102.8037 102.7785 825 0.00749906 5.715897 3_1_m_#_9_45_m 97.2585 97.2377 782 0.00137014 8.603421 3_1_m_#_4_1_#_5_1 102.3370 102.3141 823 0.00744555 -2.876692 3_1_m_#_9_26_m 104.2767 104.2517 838 0.00242971 6.821012 3_1_#_3_1_m_#_3_1_m_#_3_1_m 102.8026 102.7832 825 0.00748609 6.851128 3_1_m_#_7_7 88.7656 88.7463 714 0.00270317 2.827387 3_1_m_#_8_19 83.3883 83.3718 683 0.00177235 -5.271581 3_1_m_#_9_38_m 104.6323 104.6093 841 0.000959051 11.941556 3_1_#_9_14_m 103.2108 103.1876 830 0.000749841 -1.694085 3_1_#_9_6 102.4780 102.4520 824 0.00342591 -13.730968 3_1_#_9_29_m 104.9645 104.9426 844 0.00170585 -1.192767 3_1_m_#_9_19 104.0756 104.0579 834 0.0074896 2.840065 3_1_#_3_1_m_#_6_3 104.0051 103.9806 836 0.00749901 0.002164 3_1_m_#_9_7_m 103.2779 103.2555 828 0.0755771 11.969983 3_1_#_9_7_m 102.6738 102.6525 826 0.000749961 5.149688 3_1_#_8_1 93.9165 93.8997 753 0.00748111 -5.664189 3_1_#_9_14 103.5798 103.5549 833 0.00748194 -5.141768 3_1_#_9_47 97.5499 97.5035 471 0.00748635 -6.223240 3_1_#_3_1_#_3_1_#_3_1 101.6027 101.5762 814 0.000749837 -13.703391 3_1_m_#_6_2 80.4299 80.4144 647 0.0021862 0.563844 3_1_#_9_34 105.0644 105.0439 860 0.013751 -3.973357 3_1_#_9_46 90.9263 90.9043 729 0.00608647 -6.019686 3_1_m_#_5_2 72.5511 72.5342 581 0.000749012 -1.183369 3_1_m_#_9_16_m 103.3191 103.2939 838 0.00614573 13.658427 3_1_m_#_9_34_m 105.0644 105.0439 860 0.013751 3.973357 3_1_m_#_9_35 102.8198 102.7997 827 0.00315902 10.304795 3_1_m_#_8_5 95.3986 95.3768 768 0.00749673 -2.266418 3_1_m_#_8_17_r 97.4373 97.4130 784 0.000749996 3.398243 3_1_m_#_9_7 102.6738 102.6525 826 0.000749961 -5.149688 3_1_#_9_25_m 103.9407 103.9166 833 0.00074996 1.219869 3_1_#_8_5_m 95.3986 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0.000999855 -5.154441 10_98 89.7172 89.6969 736 0.00999706 6.815181 10_99 88.8926 88.8734 728 0.00999616 0.001240 10_100 88.7124 88.6927 744 0.00099987 5.620548 10_101 89.7344 89.7210 736 0.00999818 -9.185496 10_102 88.7969 88.7734 713 0.000979959 -1.131956 10_103 88.7971 88.7914 728 0.00999578 3.957011 10_104 89.1126 89.0919 717 0.00747675 -0.017288 10_105 89.8260 89.8055 721 0.000979897 -2.732653 10_106 88.8573 88.8387 715 0.00749995 -2.857422 10_107 89.7525 89.7356 721 0.000979942 -0.006897 10_108 88.5137 88.4932 711 0.000979928 -1.625940 10_109 89.8903 89.8723 723 0.00749988 -0.011536 10_110 89.3652 89.3438 719 0.00748647 2.778073 10_111 89.6677 89.6438 721 0.00098 -6.844370 10_112 89.5744 89.5529 719 0.000979901 2.762983 10_113 90.2239 90.2141 736 0.0099987 -3.994539 10_114 89.3062 89.2856 725 0.000998716 1.143478 10_115 90.2248 90.2035 726 0.0074971 -0.027990 10_116 90.2703 90.2583 736 0.00999239 2.719293 10_117 89.5335 89.5245 736 0.00999788 -4.018183 10_118 89.5261 89.5094 720 0.000999932 -0.007437 10_119 90.1394 90.1226 730 0.000999892 -1.253489 10_120 90.1862 90.1674 728 0.000999622 9.216600 10_121 89.9375 89.9240 872 0.000999346 4.029120 10_122 89.8258 89.8094 729 0.000998747 -1.203110 10_123 92.3646 92.3565 1498 0.0016528 -0.000064 10_124 71.0894 71.0739 576 0.000999901 -11.430135 10_125 74.9907 74.9778 616 0.00999093 0.885422 10_126 77.6202 77.6026 640 0.00999837 4.819030 10_127 80.0235 80.0124 656 0.00999296 7.542701 10_128 76.4187 76.4026 613 0.000979573 -9.842107 10_129 78.5739 78.5553 631 0.0089634 0.802389 10_130 78.8499 78.8356 704 0.000999974 3.127105 10_131 81.2871 81.2678 652 0.00899906 5.828508 10_132 74.7441 74.7330 600 0.000977062 3.475537 10_133 77.1813 77.1631 620 0.000979998 6.020808 10_134 78.6521 78.6377 648 0.0099987 -10.087952 10_135 81.2305 81.2157 657 0.000999958 0.726179 10_136 78.0398 78.0276 640 0.00999536 -1.922065 10_137 79.6352 79.6185 640 0.000979908 1.974901 10_138 82.5504 82.5320 663 0.00899595 -2.130705 10_139 72.9001 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