I love suggestion #4 (the Freemasonry/magic square one) but I suspect that the simpler first explanation is on the right track. This quibble from the article:

"But did Dürer study crystals? A systematic mathematical description of crystals begins only in the 17th century, so this theory comes at least 100 years too late."

Is really not particularly convincing when we consider what a polymath and all around genius Dürer was, and how interested he was in fine observations of nature (cf "The Great Patch of Turf.")