Knot Mosaics for the 10_65 Knot

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

The mosaic of the 1065 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.
1065 with mosaic and tile numbers realized
1065 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.