  Kagom${\'e}$ lattice is a fertile platform for topological and intertwined
electronic excitations. Recently, experimental evidence of an unconventional
charge density wave (CDW) is observed in a Z2 kagom${\'e}$ metal
AV$_{3}$Sb$_{5}$ (A= K, Cs, Rb). This observation triggers wide interests on
the interplay between frustrated crystal structure and Fermi surface
instabilities. Here we analyze the lattice effect and its impact on CDW in
AV$_{3}$Sb$_{5}$. Based on published experimental data, we show that the CDW
induced structural distortions is consistent with the theoretically predicted
inverse star-of-David pattern, which preserves the $D_{6h}$ symmetry in the
kagom${\'e}$ plane but breaks the sixfold rotational symmetry of the crystal
due to the phase shift between kagom${\'e}$ layers. The coupling between the
lattice and electronic degrees of freedom yields a weak first order structural
transition without continuous change of lattice dynamics. Our result emphasizes
the fundamental role of lattice geometry in proper understanding of
unconventional electronic orders in AV$_{3}$Sb$_{5}$.
