Stick numbers for minimal stick knots

Data for these non-equilateral case resulted from my thesis work Interactive Topological Drawing (1998). The equilateral data resulted from a collaboration with Eric Rawdon, published in a paper that appeared in Contemporary Mathematics. To view the knots in your browser window, click on the "3D view" links. This will load the knot in an interactive viewer (requires JavaScript to be enabled in your browser). If you are viewing this page in a VR-enabled browser, you'll be able to view the models in virtual reality! The lighting is a bit bad and the models are poorly placed. This will soon be fixed and additional interactivity will be implemented.

Knot Stick number Equilateral
Stick number
3D Model
(non-equilateral)
3D Model
(equilateral)
01
3
3
3D view
3D view
31
6
6
3D view
3D view
41
7
7
3D view
3D view
51
8
8
3D view
3D view
52
8
8
3D view
3D view
61
8
8
3D view
3D view
62
8
8
3D view
3D view
63
8
8
3D view
3D view
71
9
9
3D view
3D view
72
9
9
3D view
3D view
73
9
9
3D view
3D view
74
9
9
3D view
3D view
75
9
9
3D view
3D view
76
9
9
3D view
3D view
77
9
9
3D view
3D view
81
10
10
3D view
3D view
82
10
10
3D view
3D view
83
10
10
3D view
3D view
84
10
10
3D view
3D view
85
10
10
3D view
3D view
86
10
10
3D view
3D view
87
10
10
3D view
3D view
88
10
10
3D view
3D view
89
10
10
3D view
3D view
810
10
10
3D view
3D view
811
10
10
3D view
3D view
812
10
10
3D view
3D view
813
10
10
3D view
3D view
814
10
10
3D view
3D view
815
10
10
3D view
3D view
816
9
9
3D view
3D view
817
9
9
3D view
3D view
818
9
9
3D view
3D view
819
8
9
3D view
3D view
820
8
8
3D view
3D view
821
9
9
3D view
3D view
91
10
10
3D view
3D view
92
11
11
3D view
3D view
93
11
11
3D view
3D view
94
10
10
3D view
3D view
95
10
10
3D view
3D view
96
11
11
3D view
3D view
97
10
10
3D view
3D view
98
10
10
3D view
3D view
99
10
10
3D view
3D view
910
10
10
3D view
3D view
911
11
11
3D view
3D view
912
10
10
3D view
3D view
913
10
10
3D view
3D view
914
10
10
3D view
3D view
915
11
11
3D view
3D view
916
10
10
3D view
3D view
917
10
10
3D view
3D view
918
11
11
3D view
3D view
919
10
10
3D view
3D view
920
10
10
3D view
3D view
921
11
11
3D view
3D view
922
10
10
3D view
3D view
923
11
11
3D view
3D view
924
10
10
3D view
3D view
925
11
11
3D view
3D view
926
10
10
3D view
3D view
927
11
11
3D view
3D view
928
10
10
3D view
3D view
929
9
10
3D view
3D view
930
10
10
3D view
3D view
931
10
10
3D view
3D view
932
10
10
3D view
3D view
933
10
10
3D view
3D view
934
9
9
3D view
3D view
935
10
10
3D view
3D view
936
11
11
3D view
3D view
937
10
10
3D view
3D view
938
10
10
3D view
3D view
939
10
10
3D view
3D view
940
9
9
3D view
3D view
941
9
9
3D view
3D view
942
9
9
3D view
3D view
943
10
10
3D view
3D view
944
9
9
3D view
3D view
945
10
10
3D view
3D view
946
9
9
3D view
3D view
947
9
9
3D view
3D view
948
10
10
3D view
3D view
949
9
9
3D view
3D view
101
11
11
3D view
3D view
102
11
11
3D view
3D view
103
12
12
3D view
3D view
104
11
11
3D view
3D view
105
11
11
3D view
3D view
106
12
12
3D view
3D view
107
12
12
3D view
3D view
108
12
12
3D view
3D view
109
11
11
3D view
3D view
1010
12
12
3D view
3D view
1011
11
11
3D view
3D view
1012
11
11
3D view
3D view
1013
11
11
3D view
3D view
1014
11
11
3D view
3D view
1015
12
12
3D view
3D view
1016
11
12
3D view
3D view
1017
11
11
3D view
3D view
1018
12
12
3D view
3D view
1019
11
11
3D view
3D view
1020
12
12
3D view
3D view
1021
12
12
3D view
3D view
1022
12
12
3D view
3D view
1023
12
12
3D view
3D view
1024
12
12
3D view
3D view
1025
11
11
3D view
3D view
1026
12
12
3D view
3D view
1027
11
11
3D view
3D view
1028
12
12
3D view
3D view
1029
11
11
3D view
3D view
1030
12
12
3D view
3D view
1031
12
12
3D view
3D view
1032
11
11
3D view
3D view
1033
11
11
3D view
3D view
1034
12
12
3D view
3D view
1035
12
12
3D view
3D view
1036
11
11
3D view
3D view
1037
12
12
3D view
3D view
1038
12
12
3D view
3D view
1039
13
13
3D view
3D view
1040
11
11
3D view
3D view
1041
11
11
3D view
3D view
1042
11
11
3D view
3D view
1043
12
12
3D view
3D view
1044
12
12
3D view
3D view
1045
11
11
3D view
3D view
1046
12
12
3D view
3D view
1047
12
12
3D view
3D view
1048
10
10
3D view
3D view
1049
11
11
3D view
3D view
1050
12
12
3D view
3D view
1051
12
12
3D view
3D view
1052
11
11
3D view
3D view
1053
12
12
3D view
3D view
1054
12
12
3D view
3D view
1055
12
12
3D view
3D view
1056
11
11
3D view
3D view
1057
12
12
3D view
3D view
1058
12
12
3D view
3D view
1059
11
11
3D view
3D view
1060
11
11
3D view
3D view
1061
11
11
3D view
3D view
1062
12
12
3D view
3D view
1063
11
11
3D view
3D view
1064
13
13
3D view
3D view
1065
12
12
3D view
3D view
1066
12
12
3D view
3D view
1067
11
11
3D view
3D view
1068
12
12
3D view
3D view
1069
11
11
3D view
3D view
1070
12
12
3D view
3D view
1071
12
12
3D view
3D view
1072
12
12
3D view
3D view
1073
13
13
3D view
3D view
1074
12
12
3D view
3D view
1075
12
12
3D view
3D view
1076
13
13
3D view
3D view
1077
12
12
3D view
3D view
1078
12
12
3D view
3D view
1079
11
12
3D view
3D view
1080
13
13
3D view
3D view
1081
11
11
3D view
3D view
1082
12
12
3D view
3D view
1083
11
11
3D view
3D view
1084
14
14
3D view
3D view
1085
11
11
3D view
3D view
1086
11
11
3D view
3D view
1087
11
11
3D view
3D view
1088
11
11
3D view
3D view
1089
11
11
3D view
3D view
1090
11
11
3D view
3D view
1091
11
11
3D view
3D view
1092
11
11
3D view
3D view
1093
11
11
3D view
3D view
1094
11
11
3D view
3D view
1095
12
12
3D view
3D view
1096
11
11
3D view
3D view
1097
12
12
3D view
3D view
1098
11
11
3D view
3D view
1099
11
11
3D view
3D view
10100
12
12
3D view
3D view
10101
12
12
3D view
3D view
10102
10
10
3D view
3D view
10103
11
11
3D view
3D view
10104
10
10
3D view
3D view
10105
12
12
3D view
3D view
10106
11
11
3D view
3D view
10107
10
11
3D view
3D view
10108
10
10
3D view
3D view
10109
10
10
3D view
3D view
10110
12
12
3D view
3D view
10111
11
11
3D view
3D view
10112
11
11
3D view
3D view
10113
10
10
3D view
3D view
10114
10
10
3D view
3D view
10115
11
11
3D view
3D view
10116
10
10
3D view
3D view
10117
12
12
3D view
3D view
10118
11
11
3D view
3D view
10119
10
11
3D view
3D view
10120
10
10
3D view
3D view
10121
10
10
3D view
3D view
10122
10
10
3D view
3D view
10123
11
11
3D view
3D view
10124
10
10
3D view
3D view
10125
10
10
3D view
3D view
10126
11
11
3D view
3D view
10127
10
10
3D view
3D view
10128
10
10
3D view
3D view
10129
10
10
3D view
3D view
10130
10
10
3D view
3D view
10131
11
11
3D view
3D view
10132
10
10
3D view
3D view
10133
11
11
3D view
3D view
10134
10
10
3D view
3D view
10135
10
10
3D view
3D view
10136
10
10
3D view
3D view
10137
11
11
3D view
3D view
10138
11
11
3D view
3D view
10139
10
10
3D view
3D view
10140
10
10
3D view
3D view
10141
10
10
3D view
3D view
10142
11
11
3D view
3D view
10143
11
11
3D view
3D view
10144
10
10
3D view
3D view
10145
10
10
3D view
3D view
10146
10
10
3D view
3D view
10147
10
11
3D view
3D view
10148
11
11
3D view
3D view
10149
11
11
3D view
3D view
10150
10
10
3D view
3D view
10151
10
10
3D view
3D view
10152
11
11
3D view
3D view
10153
11
11
3D view
3D view
10154
11
11
3D view
3D view
10155
10
10
3D view
3D view
10156
10
10
3D view
3D view
10157
10
10
3D view
3D view
10158
10
10
3D view
3D view
10159
10
10
3D view
3D view
10160
10
10
3D view
3D view
10161
10
10
3D view
3D view
10162
10
10
3D view
3D view
10163
10
10
3D view
3D view
10164
11
11
3D view
3D view
10165
10
10
3D view
3D view


Robert G. Scharein
Centre for Experimental and Constructive Mathematics (CECM)