Table of Knot Mosaics - Mosaic Number 6 or Less


The mosaics in this table are color coded with the following key (t = tile number, tm = minimal mosaic tile number):

  • Mosaic number 5:    blue background : t = 17;
  • Mosaic number 6:    light green background : t = 22;    dark green background : t = 24;    yellow background : t = 27;    red background : tm = 32*

* Note: Most prime knots that require 32 non-blank tiles to fit on a 6-mosaic (i.e. tm = 32) have tile number less than 32 that can only be achieved on a 7-mosaic. The only knots that have mosaic number 6 and tile number 32 also have crossing number 13, and they are listed at the very bottom of the table. All given mosaics have mosaic number realized. Click "more" to see mosaics with tile number or crossing number realized.


Click mosaic for larger view.


Image
01
Image
31
Image
41
Image
51
Image
52
Image
61 (more)
Image
62
Image
63
Image
71
Image
72
Image
73 (more)
Image
74
Image
75
Image
76
Image
77
Image
81  (more)
Image
82
Image
83  (more)
Image
84
Image
85
Image
86  (more)
Image
87  (more)
Image
88  (more)
Image
89  (more)
Image
810
Image
811
Image
812
Image
813
Image
814
Image
815
Image
816
Image
817
Image
818
Image
819 (n)
Image
820
Image
821
Image
91
Image
92
Image
93  (more)
Image
94  (more)
Image
95

My mosaic number is 7

96
Image
97 (more)
Image
98
Image
99 (more)
Image
910 (more)
Image
911
Image
912 (more)
Image
913 (more)
Image
914

My mosaic number is 7

915
Image
916 (more)
Image
917

My mosaic number is 7

918
Image
919 (more)
Image
920
Image
921 (more)

My mosaic number is 7

922
Image
923
Image
924 (more)

My mosaic number is 7

925
Image
926 (more)
Image
927
Image
928

My mosaic number is 7

929

My mosaic number is 7

930
Image
931

My mosaic number is 7

932

My mosaic number is 7

933

My mosaic number is 7

934
Image
935 (more)

My mosaic number is 7

936
Image
937 (more)

My mosaic number is 7

938

My mosaic number is 7

939

My mosaic number is 7

940

My mosaic number is 7

941

My mosaic number is 7

942

My mosaic number is 7

943

My mosaic number is 7

944

My mosaic number is 7

945
Image
946 (more)

My mosaic number is 7

947
Image
948 (more)

My mosaic number is 7

949
Image
101 (more)
Image
102
Image
103 (more)
Image
104

My mosaic number is 7

105

My mosaic number is 7

106

My mosaic number is 7

107

My mosaic number is 7

108

My mosaic number is 7

109

My mosaic number is 7

1010
Image
1011 (more)
Image
1012

My mosaic number is 7

1013

My mosaic number is 7

1014

My mosaic number is 7

1015

My mosaic number is 7

1016

My mosaic number is 7

1017

My mosaic number is 7

1018

My mosaic number is 7

1019
Image
1020 (more)
Image
1021 (more)
Image
1022 (more)

My mosaic number is 7

1023

My mosaic number is 7

1024

My mosaic number is 7

1025

My mosaic number is 7

1026

My mosaic number is 7

1027
Image
1028

My mosaic number is 7

1029

My mosaic number is 7

1030

My mosaic number is 7

1031

My mosaic number is 7

1032

My mosaic number is 7

1033
Image
1034 (more)

My mosaic number is 7

1035

My mosaic number is 7

1036

My mosaic number is 7

1037

My mosaic number is 7

1038

My mosaic number is 7

1039

My mosaic number is 7

1040
Image
1041

My mosaic number is 7

1042

My mosaic number is 7

1043
Image
1044

My mosaic number is 7

1045

My mosaic number is 7

1046

My mosaic number is 7

1047

My mosaic number is 7

1048

My mosaic number is 7

1049

My mosaic number is 7

1050

My mosaic number is 7

1051

My mosaic number is 7

1052

My mosaic number is 7

1053

My mosaic number is 7

1054

My mosaic number is 7

1055

My mosaic number is 7

1056

My mosaic number is 7

1057

My mosaic number is 7

1058

My mosaic number is 7

1059

My mosaic number is 7

1060
Image
1061 (more)
Image
1062 (more)
Image
1063 (more)
Image
1064 (more)
Image
1065 (more)
Image
1066

My mosaic number is 7

1067

My mosaic number is 7

1068

My mosaic number is 7

1069

My mosaic number is 7

1070

My mosaic number is 7

1071

My mosaic number is 7

1072

My mosaic number is 7

1073
Image
1074 (more)
Image
1075
Image
1076 (more)
Image
1077 (more)
Image
1078 (more)

1079

My mosaic number is 7

1080

My mosaic number is 7

1081

My mosaic number is 7

1082

My mosaic number is 7

1083

My mosaic number is 7

1084
Image
1085

My mosaic number is 7

1086

My mosaic number is 7

1087

My mosaic number is 7

1088

My mosaic number is 7

1089

My mosaic number is 7

1090

My mosaic number is 7

1091

My mosaic number is 7

1092

My mosaic number is 7

1093

My mosaic number is 7

1094

My mosaic number is 7

1095

My mosaic number is 7

1096

My mosaic number is 7

1097

My mosaic number is 7

1098

My mosaic number is 7

1099
Image
10100

My mosaic number is 7

10101

My mosaic number is 7

10102

My mosaic number is 7

10103

My mosaic number is 7

10104

My mosaic number is 7

10105

My mosaic number is 7

10106

My mosaic number is 7

10107

My mosaic number is 7

10108

My mosaic number is 7

10109

My mosaic number is 7

10110

My mosaic number is 7

10111

My mosaic number is 7

10112

My mosaic number is 7

10113

My mosaic number is 7

10114

My mosaic number is 7

10115
Image
10116

My mosaic number is 7

10117

My mosaic number is 7

10118

My mosaic number is 7

10119

My mosaic number is 7

10120

My mosaic number is 7

10121

My mosaic number is 7

10122

My mosaic number is 7

10123
Image
10124
Image
10125
Image
10126
Image
10127

My mosaic number is 7

10128

My mosaic number is 7

10129

My mosaic number is 7

10130

My mosaic number is 7

10131

My mosaic number is 7

10132

My mosaic number is 7

10133

My mosaic number is 7

10134

My mosaic number is 7

10135

My mosaic number is 7

10136

My mosaic number is 7

10137

My mosaic number is 7

10138
Image
10139 (more)
Image
10140 (more)
Image
10141
Image
10142 (more)
Image
10143
Image
10144 (more)

10145

My mosaic number is 7

10146

My mosaic number is 7

10147
Image
10148

My mosaic number is 7

10149

My mosaic number is 7

10150

My mosaic number is 7

10151

My mosaic number is 7

10152

My mosaic number is 7

10153

My mosaic number is 7

10154
Image
10155

My mosaic number is 7

10156

My mosaic number is 7

10157

My mosaic number is 7

10158
Image
10159

My mosaic number is 7

10160

My mosaic number is 7

10161*

My mosaic number is 7

10162*

My mosaic number is 7

10163*

My mosaic number is 7

10164*

My mosaic number is 7

10165*
*These knots are listed as 10162‑10166 in Rolfsen due to the Perko Pair.        

When listing prime knots with crossing number 11 or more, we use the Dowker-Thistlethwaite name of the knot. See for more information.

All knots with mosaic number 6 and crossing number 11 are given here. None of these have tile number 32.

Image
11a43   (more)
Image
11a44   (more)
Image
11a46   (more)
Image
11a47   (more)
Image
11a58   (more)
Image
11a59   (more)
Image
11a106   (more)
Image
11a107
Image
11a139   (more)
Image
11a140
Image
11a165   (more)
Image
11a166   (more)
Image
11a179   (more)
Image
11a181   (more)
Image
11a246   (more)
Image
11a247   (more)
Image
11a339   (more)
Image
11a340   (more)
Image
11a341   (more)
Image
11a342   (more)
Image
11a343
Image
11a364   (more)
Image
11a367   (more)
Image
11n71   (more)
Image
11n72   (more)
Image
11n73   (more)
Image
11n74   (more)
Image
11n75   (more)
Image
11n76   (more)
Image
11n77   (more)
Image
11n78   (more)
 

All knots with mosaic number 6 and crossing number 12 are given here. None of these have tile number realized.

Image
12a119   (more)
Image
12a165   (more)
Image
12a169   (more)
Image
12a373   (more)
Image
12a376   (more)
Image
12a379   (more)
Image
12a380   (more)
Image
12a444   (more)
Image
12a503   (more)
Image
12a722   (more)
Image
12a803   (more)
Image
12a1148   (more)
Image
12a1149   (more)
Image
12a1166   (more)
   

All knots with mosaic number 6 and crossing number 13 are given here. Some of these have tile number 32 realized in the given mosaic.

Image
13a1230
Image
13a1236   (more)
Image
13a1461   (more)
Image
13a4573   (more)
Image
13n2399
Image
13n2400
Image
13n2401
Image
13n2402
Image
13n2403
             

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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.
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.