Knot Mosaic Space

Table of Knot Mosaics – Crossing number 10 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: dark 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*;
  • Mosaic number 7: purple background : t = 27; light blue background : t = 29; gray background : t = 31

* 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.

Click mosaic for larger view.

Circle on white background
01
curves lines on white background
31
Curved lines on blue background
41
curved lines on blue background
51
curved lines on blue background
52
Curved lines on blue background
61 (more)
Curved lines on blue background
62
Curved lines on a mint green background
63
Curved lines on a mint green background
71
Curved lines on a mint green background
72
Curved lines on a mint green background
73 (more)
Curved lines on blue background
74
Curved lines on a mint green background
75
Curved lines on a mint green background
76
Curved lines on a mint green background
77
Curved lines on a mint green background
81 (more)
Curved lines on a mint green background
82
Curved lines on a mint green background
83 (more)
Curved lines on a mint green background
84
Curved lines on green background
85
Curved lines on green background
86 (more)
Curved lines on a mint green background
87 (more)
Curved lines on a mint green background
88 (more)
Curved lines on a mint green background
89 (more)
Curved lines on green background
810
Curved lines on green background
811
Curved lines on green background
812
Curved lines on a mint green background
813
Curved lines on green background
814
Curved lines on yellow background
815
Curved lines on green background
816
Curved lines on green background
817
Curved lines on green background
818
Curved lines on green background
819
Curved lines on green background
820
Curved lines on green background
821
Curved lines
91
Curved lines on yellow background
92
Curved lines on yellow background
93 (more)
Curved lines on yellow background
94 (more)
Curved lines on a mint green background
95
Curved lines on purple background
96
Curved lines on yellow background
97 (more)
Curved lines on green background
98
Curved lines on yellow background
99 (more)
Curved lines on orange background
910 (more)
Curved lines on green background
911
Curved lines on green background
912 (more)
Curved lines on yellow background
913 (more)
Curved lines on green background
914
Curved lines on purple background
915 (more)
Curved lines on orange background
916 (more)
Curved lines on green background
917
Curved lines on purple background
918
Curved lines on purple background
919 (more)
Curved lines on a mint green background
920
Curved lines on green background
921 (more)
Curved lines on a light blue background
922
Curved lines on green background
923
Curved lines on yellow background
924 (more)
Curved lines on light blue background
925
Curved lines on green background
926 (more)
Curved lines on green background
927
Curved lines on yellow background
928
Curved lines on light blue background
929 (more)
Curved lines on light blue background
930
Curved lines on green background
931
Curved lines on light blue background
932
Curved lines on light blue background
933
Curved lines on light blue background
934
Curved lines on orange background
935 (more)
Curved lines on light blue background
936
Curved lines on yellow background
937 (more)
Curved lines on light blue background
938
Curved lines on light blue background
939
Curved lines on grey background
940
Curved lines on grey background
941
Curved lines on light blue background
942
Curved lines on light blue background
943
Curved lines on light blue background
944
Curved lines on light blue background
945
Curved lines on yellow background
946 (more)
Curved lines on light blue background
947
Curved lines on yellow background
948 (more)
Curved lines on light blue background
949
Curved lines on yellow background
101 (more)
Curved lines on yellow background
102
Curved lines on yellow background
103 (more)
Curved lines on yellow background
10 4
Curved lines on purple background
10 5 (more)
Curved lines on purple background
10 6 (more)
Curved lines on purple background
10 7 (more)
Curved lines on purple background
10 8
Curved lines on purple background
10 9 (more)
Curved lines on purple background
10 10
Curved lines on orange background
10 11 (more)
Curved lines on yellow background
10 12 (more)
Curved lines on purple background
10 13 (more)
Curved lines on purple background
10 14 (more)
Curved lines on purple background
10 15 (more)
Curved lines on purple background
10 16 (more)
Curved lines on purple background
10 17 (more)
Curved lines on purple background
10 18 (more)
Curved lines on purple background
10 19
Curved lines on orange background
10 20 (more)
Curved lines on orange background
10 21 (more)
Curved lines on yellow background
10 22 (more)
Curved lines on light blue background
10 23
Curved lines on purple background
10 24 (more)
Curved lines on purple background
10 25
Curved lines on purple background
10 26
Curved lines on light blue background
10 27
Curved lines on yellow background
10 28
Curved lines on purple background
10 29
Curved lines on purple background
10 30
Curved lines on purple background
10 31 (more)
Curved lines on purple background
10 32
Curved lines on purple background
10 33 (more)
Curved lines on yellow background
10 34 (more)
Curved lines on purple background
10 35 (more)
Curved lines on purple background
10 36 (more)
Curved lines on purple background
10 37 (more)
Curved lines on purple background
10 38 (more)
Curved lines on purple background
10 39 (more)
Curved lines on light blue background
10 40
Curved lines on green background
10 41
Curved lines on light blue background
10 42
Curved lines on light blue background
10 43
Curved lines on green background
10 44
Curved lines on light blue background
10 45
Curved lines on light blue background
10 46
Curved lines on light blue background
10 47
Curved lines on light blue background
10 48 (more)
Curved lines on light blue background
10 49
Curved lines on light blue background
10 50 (more)
Curved lines on light blue background
10 51 (more)
Curved lines on light blue background
10 52
Curved lines on light blue background
10 53
Curved lines on light blue background
10 54
Curved lines on light blue background
10 55
Curved lines on light blue background
10 56 (more)
Curved lines on light blue background
10 57
Curved lines on grey background
10 58
Curved lines on grey background
10 59
Curved lines on grey background
10 60
Curved lines on orange background
10 61 (more)
Curved lines on orange background
10 62 (more)
Curved lines on yellow background
10 63 (more)
Curved lines on orange background
10 64 (more)
Curved lines on orange background
10 65 (more)
Curved lines on yellow background
10 66
Curved lines on light blue background
10 67 (more)
Curved lines on light blue background
10 68 (more)
Curved lines on light blue background
10 69
Curved lines on light blue background
10 70 (more)
Curved lines on light blue background
10 71
Curved lines on light blue background
10 72 (more)
Curved lines on light blue background
10 73
Curved lines on orange background
10 74 (more)
Curved lines on yellow background
10 75
Curved lines on orange background
10 76 (more)
Curved lines on orange background
10 77 (more)
Curved lines on yellow background
10 78 (more)
Curved lines on light blue background
10 79 (more)
Curved lines on grey background
10 80
Curved lines on grey background
10 81
Curved lines on light blue background
10 82
Curved lines on light blue background
10 83
Curved lines on light blue background
10 84 (more)
Curved lines on green background
10 85
Curved lines on light blue background
10 86
Curved lines on light blue background
10 87
Curved lines on grey background
10 88
Curved lines on grey background
10 89
Curved lines on light blue background
10 90 (more)
Curved lines on light blue background
10 91 (more)
Curved lines on light blue background
10 92 (more)
Curved lines on light blue background
10 93 (more)
Curved lines on light blue background
10 94
Curved lines on light blue background
10 95
Curved lines on grey background
10 96
Curved lines on grey background
10 97
Curved lines on grey background
10 98
Curved lines on grey background
10 99
Curved lines on green background
10 100
Curved lines on light blue background
10 101
Curved lines on light blue background
10 102
Curved lines on light blue background
10 103 (more)
Curved lines on grey background
10 104
Curved lines on grey background
10 105
Curved lines on light blue background
10 106
Curved lines on light blue background
10 107
Curved lines on grey background
10 108
Curved lines on grey background
10 109
Curved lines on grey background
10 110
Curved lines on grey background
10 111
Curved lines on light blue background
10 112
Curved lines on light blue background
10 113
Curved lines on light blue background
10 114 (more)
Curved lines on grey background
10 115
Curved lines on green background
10 116
Curved lines on light blue background
10 117
Curved lines on grey background
10 118
Curved lines on grey background
10 119
Curved lines on grey background
10 120
Curved lines on grey background
10 121
Curved lines on grey background
10 122
Curved lines on grey background
10 123
Curved lines on green background
10 124
Curved lines on green background
10 125
Curved lines on green background
10 126
Curved lines on green background
10 127
Curved lines on light blue background
10 128
Curved lines on light blue background
10 129
Curved lines on a white background
10 130
Curved lines on light blue background
10 131
Curved lines on light blue background
10 132
Curved lines on light blue background
10 133
Curved lines on light blue background
10 134
Curved lines on light blue background
10 135
Curved lines on light blue background
10 136
Curved lines on grey background
10 137
Curved lines on grey background
10 138
Curved lines on orange background
10 139 (more)
Curved lines on yellow background
10 140 (more)
Curved lines on green background
10 141
Curved lines on yellow background
10 142 (more)
Curved lines on green background
10 143
Curved lines on yellow background
10 144 (more)
Curved lines on light blue background
10 145
Curved lines on light blue background
10 146
Curved lines on light blue background
10 147
Curved lines on green background
10 148
Curved lines on light blue background
10 149
Curved lines on light blue background
10 150
Curved lines on light blue background
10 151
Curved lines on light blue background
10 152 (more)
Curved lines on light blue background
10 153 (more)
Curved lines on grey background
10 154
Curved lines on green background
10 155
Curved lines on light blue background
10 156
Curved lines on grey background
10 157
Curved lines on light blue background
10 158 (more)
Curved lines on green background
10 159
Curved lines on light blue background
10 160
Curved lines on light blue background
10 161 *
Curved lines on light blue background
10 162 *
Curved lines on light blue background
10 163 * (more)
Curved lines on light blue background
10 164 *
Curved lines on grey background
10 165 *

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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.
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.

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