The diagrams below are two illustrations of the knot 9_10. Each is built from small tiles of five types: one is blank, two have a single arc joining points on the boundary (ether adjacent or opposite), and two have two arcs joining pairs of points on the boundary (either adjacent or opposite with an over/under crossing). The tiles can be rotated in building the overall "mosaic."
It can be proved that for 9_10 the smallest square mosaic diagram is 6 by 6. Thus, its mosaic number is 6. It used 32 nonempty tiles. The figure on the right has 27 nonempty tiles, and this is the minimum for the knot 9_10. Thus, it has tile number 27.
For much more information, visit Aaron Heap's website Knot Mosaic Space.
|Minimal Mosaic Number||Minimal Tile Number|
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 Heap, A.; LaCourt, N. Space-Efficient Prime Knot 7-Mosaics; Symmetry 2020, Vol. 12, Issue 4.
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