In my Knight's Tour Notes on Wazir tours and in various other places I included the following diagram outlining the various ways of forming a frieze with vertical and horizontal moves.
In Twitter I have been following a series of items by Tom Ruen on tiling with a wide range of various shapes. His most recent articles inspired me to put together the following two Greek Key Pattern borders. They are constructed in each case of a single rectangular (metasquare) tile pattern, in two colours and various different orientations.
Key Pattern 1
Key Pattern 2
This would make a good frame for a shaving mirror!