A crystal, having a unit$-$cell with $a=b=c,===90,$ displays the faces $(100)$ and $(012).$ Plot a stereogram showing the normal to these faces and the great circles representing their planes. Locate the pole of the zone axis of the zone containing these two faces and, by application of the zone equation, determine its indices $[$UVW$].$ The intersection of the $(111)$ plane may be apparent on these faces as slip lines. Plot the pole of $(111)$ and the great circle which represents the $(111)$ plane. Mark the intersections of the $(111)$ great circle with the $(100)$ and $(012)$ great circles. Hence determine the angles between the zone axis $[$UVW$]$ and the traces of the $(111)$ plane on $($i$)$ the $(100)$ face, and $($ii$)$ on the $(012)$ face of the crystal.