Chrysoberyl and Aragonite/Cerussite Sixlings
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EXAMP3A EXAMP3B
In reality these twins are interpenetration twins by reflection, with three individuals per twin. They can be computed in this way, but it is slower in terms of computer time, and in both cases gives a number of small extra faces which appear rather messy. Therefore these twins are most satisfactorily done with a pseudo-twin operation, which is actually the pseudo-symmetry of the twin aggregate.

Both crystals have point group MMM, orthorhombic.

For chrysoberyl, the axial lengths or ratios are 0.58 : 1 : 0.47 and the forms are:

   1)    {111}    1.0
   2)    {001}    1.0
   3)    {121}    0.97
   4)    {010}   0.5

The twin type is Contact with composition planes and there are five twins, each by rotation on axis [001], by angles of 60, 120, 180, -60 and -120 degrees. The two composition planes are (130) and (1-30) which are the true twin operators.

When completed, the twin will be lying on its back, so to speak. Select Cartesian Axes from the Rotation Menu. The axis is y and the rotation angle is 90 degrees. You must click on the Rotate button before you click on Done.
For aragonite/cerussite the axes are 0.62 : 1 : 0.72 and the forms are:

   1)    {111}    1.0
   2)    {010}    0.2
   3)    {110}   1.2

There are again five twins by successive rotation of 60 degrees about the axis [001]; however, only three of these are visible (60, 120 and -60 degrees), and no subsequent rotation is required. Although the true twin operator is reflection on 110, in the sixlings the contact plane is quite different, approximating to (-130) - for the drawing use composition planes (-8,23,0) and (-8,-23,0). These indices were chosen so that the twin individuals almost touch, and do not overlap; if they overlap, the intertwin edges will not be drawn if Remove Hidden Lines (Display menu) is selected (although removal of hidden lines is actually not necessary for this view). An alternative would be to use composition planes (-130) and (-1-30) and adjust the axial ratios. This sort of problem does not arise in real contact or interpenetration twins, only in those constructed with pseudo-operators.