  We present a novel parameter-free cosmological void finder (\textsc{dive},
Delaunay TrIangulation Void findEr) based on Delaunay Triangulation (DT), which
efficiently computes the empty spheres constrained by a discrete set of
tracers. We define the spheres as DT voids, and describe their properties,
including an universal density profile together with an intrinsic scatter. We
apply this technique on 100 halo catalogues with volumes of 2.5\,$h^{-1}$Gpc
side each, with a bias and number density similar to the BOSS CMASS Luminous
Red Galaxies, performed with the \textsc{patchy} code. Our results show that
there are two main species of DT voids, which can be characterised by the
radius: they have different responses to halo redshift space distortions, to
number density of tracers, and reside in different dark matter environments.
Based on dynamical arguments using the tidal field tensor, we demonstrate that
large DT voids are hosted in expanding regions, whereas the haloes used to
construct them reside in collapsing ones. Our approach is therefore able to
efficiently determine the troughs of the density field from galaxy surveys, and
can be used to study their clustering. We further study the power spectra of DT
voids, and find that the bias of the two populations are different,
demonstrating that the small DT voids are essentially tracers of groups of
haloes.
