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:     : t = 17;
  • Mosaic number 6:     : t = 22;     : t = 24;     : t = 27;     : 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.


01

31
41
51
52
61 (more)
62
63
71
72
7_3 Knot
73 (more)
74
75
76
77
8_1 Knot
81  (more)
8_2 Knot
82
8_3 Knot
83  (more)
8_4 Knot
84
8_5 Knot
85
8_6 Knot
86  (more)
8_7 Knot
87  (more)
8_8 Knot
88  (more)
8_9 Knot
89  (more)
8_10 Knot
810
8_11 Knot
811
8_12 Knot
812
8_13 Knot
813
8_14 Knot
814
8_15 Knot
815
8_16 Knot
816
8_17 Knot
817
818
819 (n)
820
821
91
92
93  (more)
94  (more)
95
Image

96

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

915

916 (more)
917
Image

918

919 (more)
920
921 (more)
Image

922

923
924 (more)
Image

925

926 (more)
927
928
Image

929

Image

930

931
Image

932

Image

933

Image

934

935 (more)
Image

936

937 (more)
Image

938

Image

939

Image

940

Image

941

Image

942

Image

943

Image

944

Image

945

946 (more)
Image

947

948 (more)
Image

949

101 (more)
102
103 (more)
104
Image

105

Image

106

Image

107

Image

108

Image

109

Image

1010

1011 (more)
1012
Image

1013

Image

1014

Image

1015

Image

1016

Image

1017

Image

1018

Image

1019

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

1023

Image

1024

Image

1025

Image

1026

Image

1027

1028

1029

1030

1031

1032

1033
1034 (more)

1035

1036

1037

1038

1039

1040
1041

1042

1043
1044

1045

1046

1047

1048

1049

1050

1051

1052

1053

1054

1055

1056

1057

1058

1059

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

1067

1068

1069

1070

1071

1072

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

1079

1080

1081

1082

1083

1084
1085

1086

1087

1088

1089

1090

1091

1092

1093

1094

1095

1096

1097

1098

1099
10100

10101

10102

10103

10104

10105

10106

10107

10108

10109

10110

10111

10112

10113

10114

10115
10116

10117

10118

10119

10120

10121

10122

10123
10124
10125
10126
10127

10128

10129

10130

10131

10132

10133

10134

10135

10136

10137

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

10145

10146

10147
10148

10149

10150

10151

10152

10153

10154
10155

10156

10157

10158
10159

10160

10161*

10162*

10163*

10164*

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.

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

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

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

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