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Type in your six values for the interval-class vector, then click calculate. This applet will give all pitch-class sets (containing 0) that share that interval-class vector. There will usually be twice as many sets given as there are pitches in the set (the set in all of its transpositions and inversions), but there are many sets which are cyclic (and will have less), and a few vectors that actually have more than one kind of set (which will have more).

For example:

[ 12 12 12 12 12 6 ] is the 12-pitch-class set (there is only one, because it is the same as all of its transpositions as well as its inversion).
[ 1 1 1 1 1 1 ] gives twice as many sets as may be expected, because there are two unique (transpositionally and inversionally) ways to create a set with this vector.
[ 0 0 1 1 1 0 ] gives all major and minor triads (they have the same interval-class content).