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We study the effect of atomic relaxation on the structure of moir\'e patternsin twisted graphene on graphite and double layer graphene by large scaleatomistic simulations. The reconstructed structure can be described as asuperlattice of `hot spots' with vortex-like behaviour of in-plane atomicdisplacements and increasing out-of-plane displacements with decreasing angle.These lattice distortions affect both scalar and vector potential and theresulting electronic properties. At low misorientation angles(<$\sim$1$^\circ$) the optimized structures deviate drastically from thesinusoidal modulation which is often assumed in calculations of the electronicproperties. The proposed structure might be verified by scanning probemicroscopy measurements.

Relaxation of moir\'e patterns for slightly misaligned identical lattices: graphene on graphite