Kitty Corner is diagonal from the object you are describing. Catty Corner is directly opposite to the Kitty Corner position. Therefore, Catty Corner to Kitty Corner, is Kitty Corner again, if you were in a square.
Then take a polygon - say a Heptagon. Kitty Corner to one area and Caddy Corner from that point could be two different positions.
See diagram attached.
http://img183.imagevenue.com/img.php?image=552843287_KittyvsCaddyCorner_122_459lo.jpg