  We have identified nearly a hundred close triply eclipsing hierarchical
triple star systems from data taken with the space telescope TESS. These
systems are noteworthy in that we can potentially determine their dynamical and
astrophysical parameters with a high precision. In the present paper, we report
the comprehensive study of seven new compact triply eclipsing triple star
systems taken from this larger sample: TICs 133771812, 176713425, 185615681,
287756035, 321978218, 323486857, and 650024463. Most of the data for this study
come from TESS observations, but two of them have Gaia measurements of their
outer orbits, and we obtained supplemental radial velocity (RV) measurements
for three of the systems. The eclipse timing variation curves extracted from
the TESS data, the photometric light curves, the RV points, and the spectral
energy distribution (SED) are combined in a complex photodynamical analysis to
yield the stellar and orbital parameters of all seven systems. Four of the
systems are quite compact with outer periods in the range of 41-56 days. All of
the systems are substantially flat, with mutual inclination angles of < ~2
degrees. Including the systems reported in this work, we have now studied in
considerable detail some 30 triply eclipsing triples with TESS, and are
accumulating a meaningful census of these systems.
