  The Geroch/Stephani transformation is a solution-generating transformation,
and may generate spiky solutions. The spikes in solutions generated so far are
either early-time permanent spikes or transient spikes. We want to generate a
solution with a late-time permanent spike. We achieve this by applying
Stephani's transformation with the rotational Killing vector field of the
locally rotationally symmetric Jacobs solution. The late-time permanent spike
occurs along the cylindrical axis. Using a mixed Killing vector field, the
generated solution also features a rich variety of transient structures. We
introduce a new technique to analyse these structures. Our findings lead us to
discover a transient behaviour, which we call the overshoot transition. These
discoveries compel us to revise the description of transient spikes.
