Its proponents sing the praises of the duodecimal or “dozenal” system (base twelve) over the decimal system (base ten), but only one question concerns us now.
A dozenal system requires one-digit numerals for ten and eleven, but not for twelve, since twelve would be represented by “10,” that is, one group of twelve and no units.
Brief digression: our words “eleven” and “twelve” derive from proto-Germanic *ainlif and *twalif (“one left” and “two left,” short for “ten with one left” and “ten with two left.” Both names, therefore, “come from a base ten place.”
The Dozenal Society of America and the Dozenal Society of Great Britain promote widespread adoption of the base-twelve system. They use the word "dozenal" instead of "duodecimal" because the latter comes from Latin roots that express twelve in base-ten terminology. Of course, so does “dozen,” but it’s probably rude to point that out.
Sir Isaac Pittman (1813-1898), best remembered for the Pittman system of shorthand, suggested ᘔ for “ten” and ᘍ for “eleven.” Note that the inverted 2 looks like a T (for “ten”) and the inverted 3 looks like a E (for “eleven”). Other suggestions are A for ten and B for eleven, but those look like letters amid numbers, while inverted 2 and 3 still look like numbers.
It’s best to stop here, because to go on is to get complicated: think, e.g., fractions and irrational numbers.
One last question, though -- how did the dozenal system get started? In a colony of polydactyls?
If base twelve doesn’t float your boat, does this grab you?