We present a study of the Fermi surface of KFe$_2$As$_2$ single crystals. Quantum oscillations were observed in magnetostriction measured down to 50 mK and in magnetic fields $H$ up to 14 T. For $H parallel c$, the calculated effective masses are in agreement with recent de Haas-van Alphen and ARPES experiments, showing enhanced values with respect to the ones obtained from previous band calculations. For $H parallel a$, we observed a small orbit at a cyclotron frequency of 64 T, characterized by an effective mass of $sim 0.8 m_e$, supporting the presence of a three-dimensional pocket at the Z-point.
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