Abundance determination of multiple star-forming regions in the HII
  galaxy SDSS J165712.75+321141.4
  We analyze high signal-to-noise spectrophotometric observations acquired
simultaneously with TWIN, a double-arm spectrograph, from 3400 to 10400 \AA of
three star-forming regions in the HII galaxy SDSS J165712.75+321141.4. We have
measured four line temperatures: Te([OIII]), Te([SIII]), Te([OII]), and
Te([SII]), with high precision, rms errors of order 2%, 5%, 6% and 6%,
respectively, for the brightest region, and slightly worse for the other two.
The temperature measurements allowed the direct derivation of ionic abundances
of oxygen, sulphur, nitrogen, neon and argon.
  We have computed CLOUDY tailor-made models which reproduce the O2+ measured
thermal and ionic structures within the errors in the three knots, with
deviations of only 0.1 dex in the case of O+ and S2+ ionic abundances. In the
case of the electron temperature and the ionic abundances of S+/H+, we find
major discrepancies which could be consequence of the presence of colder
diffuse gas. The star formation history derived using STARLIGHT shows a similar
age distribution of the ionizing population among the three star-forming
regions. This fact suggests a similar evolutionary history which is probably
related to a process of interaction with a companion galaxy that triggered the
star formation in the different regions almost at the same time. The hardness
of the radiation field mapped through the use of the softness parameter $\eta$
is the same within the observational errors for all three regions, implying
that the equivalent effective temperature of the radiation fields are very
similar for all the studied regions of the galaxy, in spite of some small
differences in the ionization state of different elements.
