  Based on evolutionary crystal structure searches in combination with ab
initio calculations, we predict an unusual structural phase of the
superconducting LaH$_{10}$ that is stable from about 250 GPa to 425 GPa
pressure. This new phase belongs to a trigonal $R\bar{3}m$ crystal lattice with
an atypical cell angle, $\alpha_{rhom}$ $\sim$ 24.56$^{\circ}$. We find that
the new structure contains three units of LaH$_{10}$ in its primitive cell,
unlike the previously known trigonal phase, where primitive cell contains only
one LaH$_{10}$ unit. In this phase, a 32-H atoms cage encapsulates La atoms,
analogous to the lower pressure face centred cubic phase. However, the hydrogen
cages of the trigonal phase consist of quadrilaterals and hexagons, in contrast
to the cubic phase, that exhibits squares and regular hexagons. Surprisingly,
the shortest H-H distance in the new phase is shorter than that of the lower
pressure cubic phase and of atomic hydrogen metal. We find a structural phase
transition from trigonal to hexagonal at 425 GPa, where the hexagonal crystal
lattice coincides with earlier predictions. Solving the anisotropic
Migdal-Eliashberg equations we obtain that the predicted trigonal phase (for
standard values of the Coulomb pseudopotential) is expected to become
superconducting at a critical temperature of about 175 K, which is less than
$T_c \sim$250 K measured for cubic LaH$_{10}$.
