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 = 27; Click 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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*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.