  Rovibrational bands spectra of three $\nu_{20}$, $\nu_7$ and $\nu_{19}$ bands
of 1, 3, 5 -- trioxane (H$_2$CO)$_3$ were recorded in the 50--650 cm$^{-1}$
range using a long path absorption cell coupled to a high resolution Fourier
transform spectrometer and synchrotron radiation at the AILES beamline of the
SOLEIL synchrotron. More than 16000 lines were assigned with a dRMS better than
$0.17\times10^{-3}$ cm$^{-1}$. Two different formalisms (tensorial and Watson)
were used to derive accurate rotational and quartic parameters for the three
bands and for the first time, a precise determination of Coriolis parameter and
$q_+$ $l-$doubling constant for both $\nu_{20}$ and $\nu_{19}$ perpendicular
bands was obtained. Last, each set of spectroscopic parameters is compared and
discussed between both formalisms.
