Tugtupite, space group 1¯4, belongs morphologically to the crystal class ¯42m. The paper describes pseudotrigonal contact triplets recently found as freely developed individuals on two specimens donated to the Geological Museum, Copenhagen. The contact triplets, described as a symmetric twin, have the composition planes, which are also the twin planes, (10¯1) and (01¯1); the pseudo-threefold axis, along which the crystals are pronouncedly elongate, is [111]. The calculated reentrant angles on the two sides of the pseudotrigonal prism, the protruding angle on the third side, and the ‘central misfit’, expressed as the geometrical angles, are 178° 41′, 181° 20′, and 2° 39′ respectively. Tetragonal crystals forming pseudotrigonal twins are rare and it is emphasized that the pseudotrigonal habit has become apparent only because: the faces developed on individual I and on individuals II and III are not the same; and the proportion between the lengths of the traces of the faces (¯101) individual I and (0¯11) individuals II and III in a plane perpendicular to the pseudo-threefold axis and the traces in the same plane of all other faces constituting the pseudo-threefold prism are 2:1.