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I’ve mentioned the didot point and cicero, its pica equivalent, several times on www-style during the past few years. Unlike recently added q, I’ve never really been convinced myself that it would make sense to specify these in CSS, although I suggested once in 2011 to reserve the units dd and cc (among others).
After I’ve found out that Antenna House Formatter has added support for dd and cc, I felt reminded that it would have been a good idea to add the unit at least to some optional module of CSS, because then we would need to agree on a common standard definition for it.
As it turns out, AH claims to have defined 1dd as 0.01483in. That’s exactly 0.376682mm. The traditional definition of the didot point (based upon pre-metric French inches) indeed converted to roughly 0.376 mm, which has been used as an approximation by European typesetters, but in the later 20th century it had come to mean exactly ⅜ of an millimeter, i.e. 0.375mm or 1.5q would be an approriate contemporary definition that fits well with other CSS units. Just for the record, that’s approximately 0.01476in.
I haven’t found anything about custom units in the documentations of, for instance, Prince, Vivliostyle and Weasyprint yet, by the way.
These thoughts may apply to some other typographers units as well. Most traditional English points, though, including the one used by Teχ as pt, are close enough to the Postscript/CSS definition of 1/72 inch (bp in Teχ), so a separate unit seems unnecessary.