By constructing ball-and-spoke models an attempt has been made to arrive at the atomic arrangements on the twin boundaries of four twins of calcite and one of aragonite. The Miller indices of the twins of calcite are (111), (110), (100) and (11). The twin plane in aragonite is (110). Each of the models of calcite twins has the same plane for twin plane and composition plane, and in each case it is a true mirror plane. Aragonite has a pseudo glide plane parallel to (110) gliding in the [001] direction. By making this pseudo symmetry element into a true glide plane a good model of the twin is obtained. In the (111), (110) and (100) twins of calcite all the CO3 groups in the composition plane are parallel to it. In the (11) twin the composition plane contains only CO3 groups and these are perpendicular to it.