The cells
The cycle is an X-Cycle because only a single value is involved. X is a value, so it's a variable, if you think that way. Bidirectional X-Cycles are also known as Fishy Cycles or Bilocation cycles.
The two configurations of the bidirectional cycle are enforced by two complementary, circular chains of implications. The details of each chain are given below.
Cycle details, forward direction (View 1):
{3}
Cycle details, reverse direction (View 2):
{4}
NOTE: if all hinters are selected all Bidirectional X-Cycles should (AFAIK) be found BEFORE we call the Unary Chainer, So you should (AFAIK) never see an X-Cycle hint. If all hinters are selected AND you're seeing an X-Cycle, then one of the previous (simpler) hinters has missed a trick!