The S-Curve profile can have several divisions along the time axis
87 divisions as per this image. This example has a constant positive jerk zone, a constant acceleration zone, a constant negative jerk zone, a zero acceleration zone and then the vice-versa. This is the S-Curve in its most general form
5 divisions if there exists no constant acceleration zones like t1-t2 and t5-t6
4 divisions if there exists no constant velocity (zero acceleration zone) like t3-t4
There are more possible cases that depend upon initial and final desired conditions and constraints on the positions, velocities, accelerations and jerks.
While the equations are pretty straight forward, mentioned in this paper Jeong, Soon Yong, et al. "Jerk limited velocity profile generation for high speed industrial robot trajectories." IFAC Proceedings Volumes 38.1 (2005): 595-600. for almost all possible test cases, there are issues with constant jerks and other constraints that limit the feasibility of an S-curve.