This paper introduces conjunction-forms, shapes comprised of three circles in distinct combinations of proximity, tangency, and intersection. By varying the diameters of the component circles, four discrete types of conjunction- forms produce four complete form-sets. The 200 distinct conjunction-forms are classified and illustrated in tables, and the new features and classes of forms in each form-set are examined. The author presents artworks that employ conjunction-forms and explains how artistic strategies reveal their order and structure.