Converting a 6-cycle system into a steiner triple system

Given a 6-cycle system, two ways of transforming it into a Steiner triple system have been previously considered: one can either inscribe into each 6-cycle two triangles, or one can squash each 6-cycle into two triangles. In this paper, we consider yet another way, which we call converting: delete two opposite edges of each 6-cycle and add two short diagonals to create two triangles. If, when doing this to every 6-cycle of a 6-cycle system, it …