  Using the small angle neutron scattering (SANS) technique we investigated the
vortex lattice (VL) in the mixed state of the stannide superconductor
Yb$_{3}$Rh$_{4}$Sn$_{13}$. We find a single domain VL of slightly distorted
hexagonal geometry for field strengths between 350 and 18500 G and temperatures
between T = 0.05 and T = 6.5 K. We observe a clear in-plane rotation of the VL
for different magnetic field directions relative to the crystallographic axes.
We also find that the hexagonal symmetry of the VL is energetically favorable
in Yb$_{3}$Rh$_{4}$Sn$_{13}$ for external fields oriented along axes of
different symmetries: twofold [110], threefold [111] and fourfold [100]. The
observed behavior is different from other conventional and unconventional
superconductors. The superconducting state is characterized by an isotropic
gapped order parameter with an amplitude of $\Delta(0)$ = 1.57 $\pm$ 0.05 meV.
At the lowest temperatures the field dependence of the magnetic form factor in
our material reveals a London penetration depth of $\lambda_{L}$ = 2508 $\pm$
17 $\AA$ and a Ginzburg coherence length of $\xi$ = 100 $\pm$ 1.3 $\AA$, i.e.,
it is a strongly type-II superconductor, $\kappa$ = $\lambda_{L}/\xi$ = 25.
