While a sonnet has 14 lines, a 12-line poem is identifiable in literature as a variation of the sonnet used by Elizabethan poets. Other than this example, there is no distinct term for a 12-line poem in English literature.
A sonnet is a lyric poem with 14th century roots in Italy, written in iambic pentameter and comprised of an octave of two quatrains followed by a sestet. A turn or change in the direction of the mood of the poem commonly occurs between the octave and the sestet. Two other variations of the sonnet include George Meredith's 16-line sonnets in "Modern Love" and G.M. Hopkin's 10.5-line sonnets.