Table of Knot Mosaics - Mosaic Number 6 or Less

Table of Knot Mosaics – Mosaic Number 6 or Less

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Crossing number 10 or less
Mosaic number 5 or less
Mosaic number 6 or less
Mosaic number 7 or less (Coming soon)

Click mosaic for larger view.

2-by-2 square grid of four smaller square tiles, with a single, bold black circle centered perfectly at the intersection of the grid lines. — 0₁

Interlocking black line knot on a white grid background. — 3₁

Interlocking black line knot on a blue grid background. — 4₁

Interlocking black line knot on a light green grid background. — 6₃

Interlocking black line knot on a green grid background. — 8₅

Interlocking black line knot on a light yellow grid background. — 8₁₅

Interlocking black line knot on a purple grid background. — 9₆

Interlocking black line knot on a light orange grid background. — 9₁₀听(more)

Interlocking black line knot on a light blue grid background. — 9₂₂

Interlocking black line knot on a gray grid background. — 9₄₀

curved lines on a salmon colored background — 10₆₁听(more)

curved lines on a yellow background — 10₆₃听(more)

^*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.

Curved lines on a red background — 11a₄₃听听听
(more)

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

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.

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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揔auffman 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.

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