I finally gave in and looked up the counting scheme in Fez. There are six unique 9X9 grid images that make up numbers. Three of them are completely asymmetric, and so could be rotated four different directions and yield four different images. One of them is symmetric only on one axis, so that it yields two images. And two of them are symmetric on two axes, so that they’re the same no matter which way you rotate them. That makes sixteen unique images.
So, great! Base 16; hexadecimal. This makes perfect sense, given how obsessed with computer terminology this game is. I was so convinced I had it right, and I was just waiting to find some clue that would finally shed light on which number corresponded to which pattern. Maybe it had to do with the notches on the edges of the counting cube…
But, nope. It’s base ten, with an addition scheme so that certain numbers are represented by more than one pattern. WHY THE FUCK WOULD ANYONE EXPECT A SET OF NUMERALS WHERE CERTAIN NUMBERS CAN BE WRITTEN MORE THAN ONE WAY.