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.
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