From their newsletter:
The Dozenal Society (Formerly: The Duodecimal Society) is a voluntary, non-profit, educational corporation, organized for the conduct of research and education of the public in the use of base twelve in numeration, mathematics, weights & measures, & other branches of pure & applied science.
A non-profit organization trying to promote the use of base twelve in preference to base ten. Their basic point is that 12 has a whole lot more factors than 10, and thus it's easier to work with when it comes to fractions and "decimals." Which is true, and why twelves figure so prominently in the Imperial system of weights and measures (feet, yards, pounds, ounces, etc.) It's a little impressive how they can build on essentially one point (even a decent one) to fill their journals and so forth.
They don't officially endorse particular symbols for the extra digits that duodecimal base requires. For consistency, their journal universally uses * for ten and # for eleven (which they actually call star and octothorpe. I love it). An older and also common convention is to use X for ten and E for eleven. When pronounced as digits, the new ones are "dek" and "el," respectively, with the number "10" (base twelve, or "twelve" as we commonly call it) called "do" (pronounced "dough," like the musical note).
I've subscribed from time to time, for fun. One of the cooler things I've gotten from my association with them is a few circular slide rules in base 12: that's certainly something you don't see every day! Quite cool.
The song Little Twelve-Toes from Schoolhouse Rock was dedicated to the (imagined) "International Duodecimal Society": the writer had heard of the Duodecimal Society of America (as the Dozenal Society was then called). The cartoon also uses the X and E symbols and the "dek" and "el" and "do" words.
Their address is:
The Dozenal Society of America
c/o Math Department
Nassau Community College
Garden City LI, NY 11530-6793
Their website is currently at http://members.xoom.com/harvestevia/