What a crazy project. Almost as crazy as not using QWERTY :-P

Unicode does have something that could be used: ⑽ and ⑾. They're in the enclosed alphanumerics block.

Some languages use the accent key as a dead key, which can be pretty important. But on the other hand if you use the original AltGr layer of Colemak, it helps with many accented characters, including most of the ones I use (Danish, French, Spanish). But that could be different for other languages.

Well, you asked, here goes. Dozenal (as us dozenists call it) gives us the two most common prime factors, 2 and 3. It neglects decimal's 5, which is 2/5 times less common than 3 in pure mathematical terms. 3 gives us better variety than hexadecimal's 2^4. Twelve is a SHCN, which means that it is very divisible for its size. Size is important. Base 6 would have been good, if it wasn't for it being so small. Hexadecimal is bordering on being too big, with a multiplication table with 105 non-trivial unique facts, vs. 55 for dozenal (and 36 for decimal, although we usually learn up to 12*12 (hence 55 facts) anyway).

Hexadecimal does appear to handle 3 and 5 in an okay fashion. However, this is quite deceptive. It handles 3 an 5 as well as decimal handles 3. This is not ideal, although may be considered. Unfortunately, eleven is prime, so other dozenal numbers don't benefit as much as they do in decimal, hexadecimal, or senary (senary also gains a small advantage of covering 7 (as base + 1), in the same way as "11" in any base). It is better to have proper factors, rather than omega/alpha related factors.

That explanation was probably a bit of a mess, and here is a better - but longer - document. The person who wrote it takes base choice very seriously, and has experimented with bases as high as 2520!

To reply to erw, people have drawn up symbols for ten and eleven, the most common ones being a rotated 2 or cursive X for ten, and a reversed 3 for eleven (for which I use open capital E - Ɛ). Unfortunately, there is no suitable digit ten in Unicode, and we'd also want to have all twelve digits lined up contiguously (as the decimal ones are). The enclosed alphanumerics have the problem DreymaR pointed out.

P.S. yes, it is fairly crazy.

Probably your best option is to use an embedded (or separate) numeric keypad:

<code>
9 A B
6 7 8
3 4 5
0 1 2
</code>

And you could put operations to the side, or even have rows of 4 instead of 3:

<code>
8 9 A B
4 5 6 7
0 1 2 3
</code>

Ten base comes from total number of fingers in our two hands. For ancient people, more than ten which use up all their fingers would be all classified "too many" to count.

If our two hands had twelve fingers, twelve base would be the standard base.

You know, the Dozenal Society of America's mascot is a panda. They have 6 digits on each hand, apparently. It'd be nice for typing, anyway. Imagine that, a panda on a computer!