Knot Mosaics for the 10_63 Knot

For many knots, the tile number and/or crossing number cannot be realized when the mosaic number is realized.

The mosaic of the 1063 knot given in the table has the mosaic number and tile number realized, but the crossing number of this knot cannot be realized on a 6-mosaic. The crossing number is first realized on a 7-mosaic with 29 non-blank tiles. Below are the relevant mosaics.
1063 with mosaic and tile numbers realized
1063 with crossing number realized

Back to the Knot Mosaic Table

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. Tabulating Knot Mosaics: Crossing Number 10 or Less; in preparation.