Fix(g) of Group Action on a set

Given a group action on a set X, How to find Fix(g), the set of elements in X fixed by g. The example is a simplified version based on John Fraleigh' s text Exercise 16.1

[wenjiezhou]

Hi Sir, it's Fix(delta1)={2, 4, d1, d2}.
Fix(delta1) by reflexing on diagonal d1, which leads d1, d2 and the vertices of d1 which is "2" and "4" unchanged.
Fix(delta2)={1, 3, d1, d2}.

[S]

Thanks for pointing out my error which I missed vertices 2, 4 in the fix set of delta2.

[christinedunnett]

In your last example, fix(delta2), wouldn't that be equal to the set {2, 4, d1, d2}? Rather than just {d1, d2}?