I have designed matching reversible hats for Sandy and I to wear at the Shamrock Shuffle this year (held in April of course).
The hat is designed in thirds with three simple celtic knots forming the bulk of the hat, with two shamrocks and the year in between the knots. The shamrocks and knots are regular double knitting where you have the mirror image on the reverse. The year is fancy double knitting where you can have different designs on each side.
Here you can see the bottom half of two of the knots, the year, and the chart.