The knots page explains the above terms and the notation used in the table.
Number Conway b Braid notation
L(3)10(1) 6,2,2 = 3:aaaaaaBaaB
= 3:AbbbbbbAbb
= 5:ABCbCdcBaCbbCbbD
= 6:AbCdCBaDcbCCDeDcBDCCE
L(3)10(2) 51,2,2 = 5:ABccBacbCdcBcbDc
= 5:aBccBAbDcBcdCbcc
= 3:aaBaaBBBBB
= 4:aBCCCCCCBABcB
L(3)10(3) 33,2,2 = 4:AbCbacccBccBc
= 4:abCbAccccBccB
= 4:AbbCCCbbaBcBC
= 5:ABBBBCdCbaBBCDCb
L(3)10(4) 321,2,2 = 4:AbbbCbacBccBc
= 4:AbcccBcbAbb
= 4:AbbCbbaBcBCCC
= 5:aBCdCCCBABcBDD
L(3)10(5) 222,2,2 = 4:AbbCbaccBccBc
= 4:AbccBcbbAbb
= 5:AbCdCbabbCbbDC
= 6:abCdCBAeDDCBCdEdCbC
L(3)10(6) 2211,2,2 = 5:ABcDcbaBcDcBcc
= 5:AbCbabCbdCbbCD
= 4:aaBaaBCCbCB
= 5:aBCDDDCCBABcBd
L(3)10(7) 4,4,2 = 4:abbbbCbbACBcB
= 3:AbbbbAbbbb
= 4:AbbCbbbbaBcBC
= 6:AbCCDEDcBacbCCDcBeDCC
L(3)10(8) 4,31,2 = 3:aaaaBaaBBB
= 4:abCbAcBccccBc
= 5:AbbCdcBcbbaBDcBC
= 5:aBcdCbCBABDCCCCB
L(3)10(9) 31,31,2 = 4:AbCbacBccBBBc
= 5:abccdCBACbcDcBddCd
= 4:abCbAccBccBBB
= 4:aBCCCCBBBABcB
L(3)10(10) 22,2,2,2 = 5:ABcDcbaBccBDcc
= 5:AbCbabbCdCbbCD
= 5:aBccDcBAcBdccB
= 6:abCdeDDCBACBCdEdCbC
L(3)10(11) 211,2,2,2 = 5:ABcDcBaBccBD
= 5:aBccBABDcBcD
= 5:AbbcbbabbCDCbCbd
= 5:abCddCBACBCdCbdC
L(3)10(12) 212,2,2+ = 5:ABccDcbaBccBDc
= 5:aBcDccBAcBdccB
= 5:ABcDccBaBcBD
= 4:abbCbbAcBcBcc
L(3)10(13) 3,2,2,2+ = 5:ABCdddCbaCbCdCBC
= 4:AbbACbbbccc
= 4:AbbCbbbaBccBc
= 4:aaBaaaCbbCb
L(3)10(14) 21,2,2,2+ = 5:ABccBaBDcBDD
= 4:abbCbbAcBBccB
= 5:aBcBBABDccBD
= 5:abCdCCBACBCddCbC
L(3)10(15) 4,2,2++ = 4:aaaabCbbaCB
= 4:abCbbbbAcBccB
= 5:ABccbDCbbaBcBCdc
= 6:aBcDCEdCbACBCdCbCeD
L(3)10(16) 31,2,2++ = 5:ABcDcbadcBccBdCd
= 5:abCbDcBcdbAcBccB
= 4:abCbbAcBBBccB
= 5:abCdCCCBACBCdCbC
L(3)10(17) 2,2,2+++ = 5:ABCddCbaCBdcDcbC
= 4:AbbCbaBccbbbc
= 5:AbCbaBDccBDc
= 5:abcDcBAdCBCddCbC
L(3)10(18) (4,2)(2,2) = 5:AbbCbbaDccbCdccb
= 6:abcDcBAdCBCdedCbCdE
= 3:aaBBaaBBBB
= 4:aBBBBCCBBABcB
L(3)10(19) (31,2)(2,2) = 4:AbbCbbabccccb
= 5:aBcdcBABcccDcB
= 4:AbbCCbbaBcBCC
= 5:ABBCbaCBBCCDCbCd
L(3)10(20) (3,3)(2,2) = 5:ABcDcbaCdccbCddCBd
= 5:abcDcBABdccdCbCddC
= 3:aaBBBaaBBB
= 4:aBBBCCBBBABcB
L(3)10(21) (21,21)(2,2) = 4:AbbCbbabcccbb
= 5:aBcdcBABccDccB
= 5:aBcBADccBDcB
= 5:abCddCBABCdCbCdC
L(3)10(22) (2,2++)(2,2) = 5:ABcDcbacbccDccBc
= 6:AbCCDEDcBacbcDeDcBc
= 4:AbbCCbbaBcBBC
= 5:abcDDCCCBADCBCdCbC
L(3)10(23) (2,2+)(2,2+) = 5:ABcDDcbaBccBDc
= 5:aBcDcBBAcBdccB
= 5:AbACCbbdCd
= 5:abCCbABCddCbCd
L(3)10(24) (2,2+)1(2,2) = 4:AbbCbbacBccBc
= 4:AbccBccbAbb
= 5:aBcDccBABDcB
= 5:abCddCBACBCdCbCd
L(3)10(25) (2,2),2,(2,2) = 6:ABcDEDcbacbDceddcBc
= 5:aBcdcBABBcDcBB
= 5:AbCdCCbabCCDCb
= 4:aBBCCBBABBcBB
L(3)10(26) .5 = 3:AAAAAbAbAb
= 5:ABcBcBacbCdcBcbD
= 3:AbAbAAAAAb
= 5:aBcBcBAbDcBcdCbc
L(3)10(27) .32 = 4:AbCbCbaBcBCCC
= 4:ABcbAbbbAcBcb
= 4:abCbCbACBcBCC
= 4:abCbbbAcBcBcB
L(3)10(28) .221 = 4:AbAcBBBAbcBAbcB
= 5:ABcBcBaBcdcBcD
= 4:abCbCbACBBcBC
= 5:abcDcBABcBcBDc
L(3)10(29) .3.3 = 4:AbCbCCCbaBcBC
= 4:AbCbaBcBcccBc
= 3:AbAbAAAbbb
= 5:ABcbDCbCbaBcBCdc
L(3)10(30) .3.30 = 3:AAAbAAAbAb
= 5:ABCdccbaCBdcDcbCdC
= 4:AbCbaBcBcBBBc
= 4:abCbAcBcBcBBB
L(3)10(31) .3:3 = 4:abCbAcBcBBBcB
= 4:AbCbaBcBBBcBc
= 4:AbCbaBcBBBcBc
= 4:abCbAcBcBBBcB
L(3)10(32) .3:30 = 3:AAAbAbbbAb
= 5:AbCbaBcBDCbCdcBc
= 3:AbbbAbAAAb
= 5:AbCdcBcbDCbaBcBC
L(3)10(33) .21:210 = 4:AbCCbaaabCb
= 5:ABcDcBcdcBaBcB
= 4:aaBBCbaBCbCCB
= 5:AbACbdCbdC
L(3)10(34) .4:20 = 5:ABcDcbaCdcBCdccBcd
= 3:AAAAbAbbAb
= 5:abcDcBAdCCBcdCBcBC
= 3:AbbAbAAAAb
L(3)10(35) .31:20 = 4:AbCbaaaabCb
= 4:AbCbbCbaBcBCC
= 4:aaaBBCbaBCbCB
= 4:abCbbCbACBcBC
L(3)10(36) .22:2 = 5:AbACbcddCbccDc
= 4:AABcbAbbAcBcb
= 5:abCdCbACBCdCbC
= 4:abCbbAcBcBBcB
L(3)10(37) .2.3.20 = 4:AbcBcbABcccbb
= 4:AbbCbCCbaBcBC
= 5:AbCDcDCbaCCbCdCBDc
= 3:AbbAbAAbbb
L(3)10(38) .(2,2):20 = 5:ABcDcBacbccdccBc
= 5:aBcDcBABcDcB
= 4:aaBBCbaaBCbCB
= 5:aBcDDCBcBACBCdCbCC
L(3)10(39) .(2,2+) = 5:ABCdCdCbaCbCdCBC
= 4:AbAcccbbACb
= 5:ABcDcBaBDcBD
= 4:abbCbbAcBcBcB
L(3)10(40) 20.2.20.20 = 3:AAbbAbbAbb
= 5:abCbbDCbAbCdCb
= 5:aBcdCCBABBcBDCCB
= 4:AbccBcbbAbbcB
L(3)10(41) 8*2.2 = 5:aBcBDcBABcdcBc
= 4:AbbcBcbABcbAb
= 3:AAbbAbAbAb
= 4:aBaBCbaBCCbCB
L(3)10(42) 8*2::2 = 5:aBcBDcBABcBdcB
= 4:AbcBcbABcbAAb
= 3:AAbAbAAbAb
= 4:aBaCCbCbbaBCb
L(3)10(43) 6,2,2- = 3:aaaaaaBAAB
= 3:abbabbbbbb
= 5:ABCbCdcBaCBBCbbD
5 6:AbCdCBaDcbCCDedcBdCCE
L(3)10(44) 51,2,2- = 5:ABCCBacbCdcBcbDc
= 5:abccbAbDcBcdCbcc
= 3:aaBAABBBBB
3 4:aBCCCCCCBAbcb
L(3)10(45) 33,2,2- = 4:AbCbacccBCCBc
= 4:abCbAccccbccb
= 4:ABBCCCbbaBcBC
4 5:ABBBBCdcbaBBcDCb
L(3)10(46) 321,2,2- = 4:AbbbCbacBCCBc
= 4:abbabcccBcb
= 4:AbbCBBaBcBCCC
4 5:aBCdCCCBAbcbDD
L(3)10(47) 222,2,2- = 4:AbbCbaccBCCBc
= 4:abbabccBcbb
= 5:AbCdCbabbCBBDC
5 6:abCdCBAeDDcBCdEdCbc
L(3)10(48) 2211,2,2- = 5:ABcDcbaBcDcBCC
= 5:AbCbabCbdcbbcD
= 4:aaBAABCCbCB
4 5:aBCDDDCCBAbcbd
L(3)10(49) 4,4,2- = 4:abbbbCBBACBcB
= 3:abbbbabbbb
= 4:ABBCbbbbaBcBC
4 6:AbCCdEDcBacbCCDcBedCC
L(3)10(50) 4,31,2- = 3:aaaaBAABBB
= 4:abCbAcbccccbc
= 5:ABBCdcBcbbaBDcBC
4 5:aBcdCbCBAbDCCCCb
L(3)10(51) 31,31,2- = 4:AbCbacBCCBBBc
= 5:abccdCBAcbcDcBddcd
= 4:abCbAccBCCBBB
3 4:aBCCCCBBBAbcb
L(3)10(52) 22,2,2,2- = 5:ABcDcbaBccBDCC
= 5:AbCbabbCdcbbcD
= 5:aBCCDcBAcBdccB
5 6:abcdeDDcBACBCdEdCbC
L(3)10(53) 211,2,2,2- = 5:ABcDcBaBCCBD
= 5:abccbABDcBcD
= 5:ABBcbbabbCDCbCbd
= 5:abCddCBAcBCdCbdc
L(3)10(54) 22,2,2,2-- = 5:ABcDcbabccbDCC
= 5:AbCbabbCdcBBcD
= 5:aBCCDcBAcBdCCB
5 6:abcdeDDcBAcBCdEdCbc
L(3)10(55) (4,2)(2,2-) = 5:AbbCBBaDccbCdccb
5 6:abcDcBAdCBcdedcbCdE
= 3:aaBBAABBBB
3 4:aBBBBCCBBAbcb
L(3)10(56) (31,2)(2,2-) = 4:ABBCbbabccccb
4 5:aBcdcBAbcccDcb
= 4:AbbCCBBaBcBCC
4 5:ABBCbaCBBCCDcbcd
L(3)10(57) (3,3)(2,2-) = 5:ABcDcbaCdccbCDDCBd
= 5:abcDcBABdccdCbcddc
= 3:aaBBBAABBB
3 4:aBBBCCBBBAbcb
L(3)10(58) (21,21)(2,2-) = 4:ABBCbbabcccbb
4 5:aBcdcBAbccDccb
= 5:aBcBADCCBDcB
= 5:abcddcBABCdCbCdC
L(3)10(59) (3,21-)(2,2) 4 5:ABcDcbaCCDcbCddCBd
4 5:abcDcBABdcDCCbCddC
= 3:aabbbaaBBB
= 4:aBBBCCbbbABcB
L(3)10(60) (2,2++)(2,2-) = 5:ABcDcbacbccDCCBc
5 6:AbCCdEDcBacbcDedcBc
= 4:ABBCCbbaBcBBC
4 5:abcDDCCCBADCBcdcbC
L(3)10(61) (4,2)-(2,2) = 5:ABBCBBaDccbCdccb
5 6:abcDcBAdcBcdedcbcdE
= 3:AABBAABBBB
= 4:aBBBBCBBAbccb
L(3)10(62) (31,2)-(2,2) = 4:ABBCBBabccccb
4 5:abcdcbAbcccDcb
= 4:ABBCCBBaBcBCC
= 5:ABCCDcbbacBBdCbC
L(3)10(63) (3,3)-(2,2) = 5:ABcDcbaCdccbcDDcBd
= 5:abcDcBABdccdCbcDDc
= 3:AABBBAABBB
= 4:aBBBCBBBAbccb
L(3)10(64) (21,21)-(2,2) = 4:ABBCBBabcccbb
4 5:abcdcbAbccDccb
= 5:aBcBAdCCBdcB
= 5:abcDDcBABCdCbCdC
L(3)10(65) (2,2++)-(2,2) = 5:ABcDcbacbCCDCCBc
5 6:AbCCdEdcBacbcdedcBc
= 4:ABBCCBBaBcBBC
4 5:abcDDCCCBADcBcdcbc
L(3)10(66) (2,2),2,(2,2-) 5 6:ABcDEDcbaCbDceddcBC
= 5:aBcdcBABBcDcbb
3 5:ABCdCCBabCCDCb
3 4:aBBCCBBAbbcBB
L(3)10(67) (2,2),-2,(2,2) 4 6:ABcDEdcbacbdceddcBc
4 5:abcdcbABBcDcBB
4 5:AbcdCCbabCCDcb
= 4:aBBCBBABBccBB
L(3)10(68) (2,2),2,-(2,2) 5 6:ABCDEDCbaCbDceddcBC
= 5:aBcdcBAbbcDcbb
4 5:ABCdCCBaBCCDCB
= 4:aBBCCBBAbbcbb
L(3)10(69) (2,2-),2,(2,2-) 4 6:ABcDEDcbaCbDCeddCBC
4 5:aBCdcBABBcDCbb
4 5:ABCdccBabCCDCb
= 4:aBBCCbbAbbcBB
L(3)10(70) .(2,2-):20 = 5:ABcDcBacbCCdccBc
= 5:aBcDcBAbcDcb
= 4:aaBBCbAABCbCB
4 5:aBcDDCBcBACBcdcbCC
L(3)10(71) .-(2,2):20 = 5:ABcDcBacbCCdCCBc
= 5:abcDcbAbcDcb
= 4:AABBCbAABCbCB
= 5:aBcDCBcBACBcddcbCC
L(3)10(72) 20.-2.-20.20 = 3:AABBAbbABB
4 5:abcbbDcbAbcdcb
4 5:ABcDCCbbaCBBCdcb
= 4:AABaBBCbbaBCb
Back to the Knots page
Home to Adam Chalcraft's home page