The AHD has this for the etymology of diet (http://www.bartleby.com/61/36/D0213600.html):

Middle English diete, from Old French, from Latin diaeta, way of living, diet, from Greek diaita, back-formation from diaitsthai, to live one's life, middle voice of diaitn, to treat.

So it looks like maahey is right.

The Irregularity in question is having sides of different lengths.

Bingley

Bingley