  The paper is devoted to the memory of Igor E. Dzyaloshinsky. In our common
paper I.E. Dzyaloshinskii and G.E. Volovick, Poisson brackets in condensed
matter, Ann. Phys. {\bf 125} 67--97 (1980), we discussed the elasticity theory
described in terms of the gravitational field variables -- the elasticity
vielbein $E_\mu^a$. They come from the phase fields, which describe the
deformations of crystal. The important property of the elasticity vielbein
$E^a_\mu$ is that in general they are not the square mstrices. While the
spacetime index $\mu$ takes the values $\mu=(0,1,2,3)$, in crystals the index
$a=(1,2,3)$, in vortex lattices $a=(1,2)$, and in smectic liquid crystals there
is only one phase field, $a=1$. These phase fields can be considered as the
spin gauge fields, which are similar to the gauge fields in Standard Model (SM)
or in Grand Unification (GUT).
  On the other hand, the rectangular vielbein $e^\mu_a$ may emerge in the
vicinity of Dirac points in Dirac materials. In particular, in the planar phase
of the spin-triplet superfluid $^3$He the spacetime index $\mu=(0,1,2,3)$,
while the spin index $a$ takes values $a=(0,1,2,3,4)$. Although these $(4
\times 5)$ vielbein describing the Dirac fermions are rectangular, the
effective metric $g^{\mu\nu}$of Dirac quasiparticles remains (3+1)-dimensional.
All this suggests the possible extension of the Einstein-Cartan gravity by
introducing the rectangular vielbein, where the spin fields belong to the
higher groups, which may include SM or even GUT groups.
