A mustache which connects, either along the jawline or along the upper cheek, with the sideburns before continuing over the ears and around the back of the head. Note that the remainder of the head must be shaved to qualify as an infinistache.
I was with my friend at dinner the other night when a young couple with a newborn came into the restaurant and sat near us. I was just about to touch on the true meaning of life when she went blue-screen on me and was staring at the gurgling, cooing infant. A typical case of infanity, it would seem.