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Plotting poles
by the
intersection of
a small circle
and a great circle

Suppose we wish to plot the pole 121

The angle between this pole and 001 is cos−1 (1/√6) which is 65.91°, so we draw the small circle with this angle around 001.

Method 1

We then construct the great circle passing through 001 and 121. This great circle also passes through 120 and is a diameter of the stereogram. The angle between 120 and 010 is cos−1 (2/√5) = 26.57°. Therefore, the relevant diameter is one which makes an angle of 26.57° with the diameter passing through 010, 001 and 010.

Method 1

We then construct the great circle passing through 001 and 121. This great circle also passes through 120 and is a diameter of the stereogram. The angle between 120 and 010 is cos−1 (2/√5) = 26.57°. Therefore, the relevant diameter is one which makes an angle of 26.57° with the diameter passing through 010, 001 and 010.

The small circle around 001 and the great circle we have just drawn intersect at 121 (and 121, but we can discount this as an answer because it would clearly be wrong).

Method 2

121 lies on the great circle whose pole is 101.

To plot this great circle, rotate the Wulff net by 90°.

Draw the 101 great circle. This great circle passes through 010, 121 ,111, 111 and 010, as shown.

The small circle around 001 and the great circle we have just drawn intersect at 121 (and 121, but we can discount this as an answer because it would clearly be wrong).