Table of Knot Mosaics - Crossing number 10 or less
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The mosaics in this table are color coded with the following key (t = tile number, tm = minimal mosaic tile number):
* Note: Prime knots that require 32 non-blank tiles to fit on a 6-mosaic (i.e. tm = 32) may have tile number less than 32 that can only be achieved on a 7-mosaic. All given mosaics have mosaic number realized. Click "more" to see mosaics with tile number or crossing number realized. |
: t = 17;
: t = 22; 
: t = 24; 
: t = 27; 
: tm = 32*;
: t = 27; 
: t = 29; 
: t = 31Click mosaic for larger view.
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Image
01 |
Image
31 |
Image
41
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Image
51
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Image
52
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Image
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Image
62
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Image
|
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Image
71
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Image
72
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Image
73 (more)
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Image
74
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Image
75
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Image
76
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Image
77
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Image
81 (more)
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Image
82
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Image
83 (more)
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Image
84
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Image
85
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Image
86 (more)
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Image
87 (more)
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Image
88 (more)
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Image
89 (more)
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Image
810
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Image
811
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Image
812
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Image
813
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Image
814
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Image
815
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Image
816
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Image
817
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Image
818
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Image
819
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Image
820
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Image
821
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Image
91
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Image
92
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Image
93 (more)
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Image
94 (more)
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Image
95
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Image
96
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Image
97 (more)
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Image
98
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Image
99 (more)
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Image
910 (more)
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Image
911
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Image
912 (more)
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Image
913 (more)
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Image
914
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Image
915 (more)
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Image
916 (more)
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Image
917
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Image
918
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Image
919 (more)
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Image
920
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Image
921 (more)
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Image
922
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Image
923
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Image
924 (more)
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Image
925
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Image
926 (more)
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Image
927
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Image
928
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Image
929 (more)
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Image
930
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Image
931
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Image
932
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Image
933
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Image
934
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Image
935 (more)
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Image
936
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Image
937 (more)
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Image
938
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Image
939
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Image
940
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Image
941
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Image
942
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Image
943
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Image
944
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Image
945
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Image
946 (more)
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Image
947
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Image
948 (more)
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Image
949
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Image
101 (more)
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Image
102
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Image
103 (more)
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Image
104
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Image
105 (more)
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Image
106 (more)
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Image
107 (more)
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Image
108
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Image
109 (more)
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Image
1010
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Image
1011 (more)
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Image
1012 (more)
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Image
1013 (more)
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Image
1014 (more)
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Image
1015 (more)
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Image
1016 (more)
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Image
1017 (more)
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Image
1018 (more)
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Image
1019
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Image
1020 (more)
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Image
1021 (more)
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Image
1022 (more)
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Image
1023
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Image
1024 (more)
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Image
1025
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Image
1026
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Image
1027
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Image
1028
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Image
1029
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Image
1030
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Image
1031 (more)
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Image
1032
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Image
1033 (more)
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Image
1034 (more)
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Image
1035 (more)
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Image
1036 (more)
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Image
1037 (more)
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Image
1038 (more)
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Image
1039 (more)
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Image
1040
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Image
1041
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Image
1042
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Image
1043
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Image
1044
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Image
1045
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Image
1046
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Image
1047
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Image
1048 (more)
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Image
1049
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Image
1050 (more)
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Image
1051 (more)
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Image
1052
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Image
1053
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Image
1054
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Image
1055
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Image
1056 (more)
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Image
1057
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Image
1058
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Image
1059
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Image
1060
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Image
1061 (more)
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Image
1062 (more)
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Image
1063 (more)
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Image
1064 (more)
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Image
1065 (more)
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Image
1066
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Image
1067 (more)
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Image
1068 (more)
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Image
1069
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Image
1070 (more)
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Image
1071
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Image
1072 (more)
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Image
1073
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Image
1074 (more)
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Image
1075
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Image
1076 (more)
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Image
1077 (more)
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Image
1078 (more)
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Image
1079 (more)
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Image
1080
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Image
1081
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Image
1082
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Image
1083
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Image
1084 (more)
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Image
1085
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Image
1086
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Image
1087
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Image
1088
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Image
1089
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Image
1090 (more)
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Image
1091 (more)
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Image
1092 (more)
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Image
1093 (more)
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Image
1094
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Image
1095
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Image
1096
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Image
1097
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Image
1098
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Image
1099
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Image
10100
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Image
10101
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Image
10102
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Image
10103 (more)
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Image
10104
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Image
10105
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Image
10106
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Image
10107
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Image
10108
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Image
10109
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Image
10110
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Image
10111
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Image
10112
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Image
10113
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Image
10114 (more)
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Image
10115
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Image
10116
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Image
10117
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Image
10118
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Image
10119
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Image
10120
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Image
10121
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Image
10122
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Image
10123
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Image
10124
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Image
10125
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Image
10126
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Image
10127
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Image
10128
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Image
10129
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Image
10130
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Image
10131
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Image
10132
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Image
10133
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Image
10134
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Image
10135
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Image
10136
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Image
10137
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Image
10138
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Image
10139 (more)
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Image
10140 (more)
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Image
10141
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Image
10142 (more)
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Image
10143
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Image
10144 (more)
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Image
10145
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Image
10146
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Image
10147
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Image
10148
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Image
10149
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Image
10150
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Image
10151
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Image
10152 (more)
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Image
10153 (more)
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Image
10154
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Image
10155
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Image
10156
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Image
10157
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Image
10158 (more)
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Image
10159
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Image
10160
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Image
10161*
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Image
10162*
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Image
10163* (more)
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Image
10164*
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Image
10165*
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*These knots are listed as 10162‑10166 in Rolfsen due to the Perko Pair. | |||||
References:
Heap, A.; Knowles, D. Tile Number and Space-Efficient Knot Mosaics; J. Knot Theory Ramif. 2018, 27.
Heap, A.; Knowles, D. Space-Efficient Knot Mosaics for Prime Knots with Mosaic Number 6; Involve 2019, 12.
Heap, A.; LaCourt, N. Space-Efficient Prime Knot 7-Mosaics; Symmetry 2020, 12.
Heap, A.; Baldwin, D.; Canning, J.; Vinal, G. Tabulating Knot Mosaics: Crossing Number 10 or Less; in preparation.
Kuriya, T.; Shehab, O. The Lomonaco–Kauffman Conjecture; J. Knot Theory Ramif. 2014, 23.
Lee, H.; Ludwig, L.; Paat, J.; Peiffer, A. Knot Mosaic Tabulation; Involve 2018, 11.
Lomonaco, S.J.; Kauffman, L.H. Quantum Knots and Mosaics; Quantum Inf. Process. 2008, 7, 85–115.
Ludwig, L.; Evans, E. An Infinite Family of Knots Whose Mosaic Number Is Realized in Non-reduce Projections; J. Knot Theory Ramif. 2013, 22.
Rolfsen, D. Knots and Links; Publish or Perish Press: Berkeley, CA, USA, 1976.