Fig. 1

Formation of the X–Y–Z coordinated three reference planes, perpendicular to each other and based on the lower second molar structures. a, b Horizontal plane, illustrated by the horizontal line, was set to tangent the disto-lingual and disto-buccal cusp tips, as seen in a coronal view in (a), and at the same time also the mesio-lingual cusp tip, as seen in sagittal view in (b). c, d. Frontal plane, set to touch the most distal point of the crown, is shown as a vertical line in a sagittal view in (c) and as a horizontal line in an axial view in (d). a, d Sagittal plane, set to touch the lingual wall of the crown, is shown by the vertical lines in a frontal view in (a) and in an axial view in (d)