  We present X-ray spectral analyses for three Seyfert 2 active galactic
nuclei, NGC 424, NGC 1320, and IC 2560, observed by NuSTAR in the 3-79 keV
band. The high quality hard X-ray spectra allow detailed modeling of the
Compton reflection component for the first time in these sources. Using
quasi-simultaneous NuSTAR and Swift/XRT data, as well as archival XMM-Newton
data, we find that all three nuclei are obscured by Compton-thick material with
column densities in excess of ~5 x $10^{24}$ cm$^{-2}$, and that their X-ray
spectra above 3 keV are dominated by reflection of the intrinsic continuum on
Compton-thick material. Due to the very high obscuration, absorbed intrinsic
continuum components are not formally required by the data in any of the
sources. We constrain the intrinsic photon indices and the column density of
the reflecting medium through the shape of the reflection spectra. Using
archival multi-wavelength data we recover the intrinsic X-ray luminosities
consistent with the broadband spectral energy distributions. Our results are
consistent with the reflecting medium being an edge-on clumpy torus with a
relatively large global covering factor and overall reflection efficiency of
the order of 1%. Given the unambiguous confirmation of the Compton-thick nature
of the sources, we investigate whether similar sources are likely to be missed
by commonly used selection criteria for Compton-thick AGN, and explore the
possibility of finding their high-redshift counterparts.
