Knot Mosaics for the 10<sub>78</sub> Knot

Knot Mosaics for the 10₇₈ Knot

For many knots, the tile number and/or crossing number cannot be realized when the mosaic number is realized. The mosaic of the 10₇₈ knot given in the table has the mosaic number (6) and tile number (27) realized, but the crossing number of this knot cannot be realized with only 27 non-blank tiles. The crossing number is first realized on a 6-mosaic with 32 non-blank tiles, but it can also be realized on a 7-mosaic with 29 non-blank tiles. Below are the relevant mosaics.

10₇₈ with mosaic and tile numbers realized			10₇₈ with crossing number realized on a 6-mosaic with 32 non-blank tiles			10₇₈ with crossing number realized on a 7-mosaic with 29 non-blank tiles

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References:

Heap, A.; Knowles, D. Space-Efficient Knot Mosaics for Prime Knots with Mosaic Number 6; Involve 2019, 12.
Heap, A.; Baldwin, D.; Canning, J.; Vinal, G. Knot Mosaics For Prime Knots with Crossing Number 10 or Less; in preparation.