An unknown mineral shows three distinct pleochroic colours. Explain what observations you need to make in order to decide which crystal system it belongs to.

If it has three pleochroic colours this means that it must have a biaxial indicatrix and must therefore be orthorhombic, monoclinic or triclinic. In order to work out which one of these it is you need to work out the orientation of the indicatrix with respect to the crystallographic axes but I'm not sure how you can do this. You can measure the extinction angle with respect to things like cleavage but if its an unknown mineral then you don't know how the cleavage is oriented with respect to the axes. How do you determine which direction the crystallographic axes are in using a petrographic microscope?

An unknown mineral shows three distinct pleochroic colours. Explain what observations you need to make in order to decide which crystal system it belongs to.

If it has three pleochroic colours this means that it must have a biaxial indicatrix and must therefore be orthorhombic, monoclinic or triclinic. In order to work out which one of these it is you need to work out the orientation of the indicatrix with respect to the crystallographic axes but I'm not sure how you can do this. You can measure the extinction angle with respect to things like cleavage but if it's an unknown mineral then you don't know how the cleavage is oriented with respect to the axes. How do you determine which direction the crystallographic axes are in using a petrographic microscope?