  We study the nature of voids defined as single-stream regions that have not
undergone shell-crossing. We use ORIGAMI to determine the cosmic web morphology
of each dark matter particle in a suite of cosmological $N$-body simulations,
which explicitly calculates whether a particle has crossed paths with others
along multiple sets of axes and does not depend on a parameter or smoothing
scale. The theoretical picture of voids is that of expanding underdensities
with borders defined by shell-crossing. We find instead that locally underdense
single-stream regions are not bounded on all sides by multi-stream regions,
thus they percolate, filling the simulation volume; we show that the set of
multi-stream particles also percolates. This percolation persists to high
resolution, where the mass fraction of single-stream voids is low, because the
volume fraction remains high; we speculate on the fraction of collapsed mass in
the continuum limit of infinite resolution. By introducing a volume threshold
parameter to define underdense void "cores", we create a catalog of ORIGAMI
voids which consist entirely of single-stream particles and measure their
percolation properties, volume functions, and average densities.
