Knot Mosaics for the 1024 Knot

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

The mosaic of the 1024 knot given in the table has the mosaic number and tile number realized, but the crossing number of this knot cannot be realized when the tile number (27) is. The crossing number is first realized with 29 non-blank tiles. Below are the relevant mosaics.

1024 with mosaic and tile numbers realized
1024 with crossing number realized

Back to the Knot Mosaic Table

References:

Heap, A.; LaCourt, N. Space-Efficient Prime Knot 7-Mosaics; Symmetry 2020, 12.
Heap, A.; Baldwin, D.; Canning, J.; Vinal, G. Knot Mosaics For Prime Knots with Crossing Number 10 or Less; in preparation.

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