  The explosion processes of supernovae (SNe) are imprinted in their explosion
geometries. Here, we study the intrinsic polarization of 15 hydrogen-rich
core-collapse SNe and explore the relation with the photometric and
spectroscopic properties. Our sample shows diverse properties of the continuum
polarization. The polarization of most SNe has a low degree at early phases but
shows a sudden rise to $\sim 1$ \% degree at certain points during the
photospheric phase as well as a slow decline during the tail phase, with a
constant polarization angle. The variation in the timing of peak polarisation
values implies diversity in the explosion geometry: some SNe have aspherical
structures only in their helium cores, while in other SNe these reach out to a
significant part of the outer hydrogen envelope with a common axis from the
helium core to the hydrogen envelope. Other SNe show high polarization from
early phases and a change of the polarization angle around the middle of the
photospheric phase. This implies that the ejecta are significantly aspherical
to the outermost layer and have multi-directional aspherical structures.
Exceptionally, the Type~IIL SN~2017ahn shows low polarization at both the
photospheric and tail phases. Our results show that the timing of the
polarization rise in Type~IIP SNe is likely correlated with their brightness,
velocity and the amount of radioactive Ni produced: brighter SNe with faster
ejecta velocity and a larger $^{56}$Ni mass have more extended-aspherical
explosion geometries. In particular, there is a clear correlation between the
timing of the polarization rise and the explosion energy, that is, the
explosion asphericity is proportional to the explosion energy. This implies
that the development of a global aspherical structure, e.g., a jet, might be
the key to realising an energetic SN in the mechanism of SN explosions.
