  A knot mosaic is a representation of a knot or link on a square grid using a
collection of tiles that are either blank or contain a portion of the knot
diagram. Traditionally, a piece of the knot on one tile connects to a piece of
the knot on an adjacent tile at a connection point that is located at the
midpoint of a tile edge. We introduce a new set of tiles in which the
connection points are located at corners of the tile. By doing this, we can
create more efficient knot mosaics for knots with small crossing number. In
particular, when using these corner connection tiles, it is possible to create
knot mosaic diagrams for all knots with crossing number 8 or less on a mosaic
that is no larger and uses fewer non-blank tiles than is possible using the
traditional tiles.
