Indeed, I was sitting in my cubicle at work thinking about cubical quads...
I suspect the description you remember is not quite correct.
I often use a cubical quad for 2m on my car, but that is about the lowest
band for which it is practical. This antenna is about 20 inches on a
side and about 14 inches long - close to a cube, but not exact. That
is for 2 elements. I've used versions up to 5 elements long, but they
need a much stronger support if you are going to use them at highway
speeds. Many of the transmitter hunters in southern California use a
4-element design developed by the late K6OPS and published in K0OV's
book on transmitter hunting.
An excellent description of quad antennas by W4RNL is found here:http://www.cebik.com/quad/2mq.html
I've found that his 3-element design works as well as the K6OPS design
(who didn't have the advantage of computer modelling in the 1950's)
and gives me direct coax feed on a shorter boom. In fact, W4RNL even
has a spreadsheet you can use to calculate optimized quad dimensions
by enterying the desired frequency and element diameter - look here:http://www.cebik.com/trans/ant-design.html
(There are a number of "quad calculators" available online. Don't trust
any of them that doesn't correct for the diameter of the element wire.)
There are other antenna variants as well. While you can shrink a quad
loop to about half the original dimension (but with the same boom
length) and still have a usable antenna, you can't make a 20m beam
quite as small as you were describing.