Knot Mosaics for the 10_56 Knot
For many knots, the tile number and/or crossing number cannot be realized when the mosaic number is realized.
The mosaic of the 1056Ìýknot given in the table has the mosaic number and tile number realized, but theÌýcrossing number of this knot cannot be realized when the tile number is 29. The crossing number is first realized with 31 non-blank tiles. Below are the relevant mosaics.


References:
Heap, A.; Baldwin, D.; Canning, J.; Vinal, G.ÌýTabulating Knot Mosaics: Crossing Number 10 or Less; in preparation.