  I search for the ground state structures of the kagome metals KV$_3$Sb$_5$,
RbV$_3$Sb$_5$, and CsV$_3$Sb$_5$ using first principles calculations.
Group-theoretical analysis shows that there are seventeen different distortions
that are possible due to the phonon instabilities at the $M$
$(\frac{1}{2},0,0)$ and $L$ $(\frac{1}{2},0,\frac{1}{2})$ points in the
Brilouin zone of the parent $P6/mmm$ phase of these materials. I generated
these structures for the three compounds and performed full structural
relaxations that minimize the atomic forces and lattice stresses. I find that
the $Fmmm$ phase with the order parameter $M_1^+$ $(a,0,0)$ $+$ $L_2^-$
$(0,b,b)$ has the lowest energy among these possibilities in all three
compounds. However, the $Fmmm$ exhibits a dynamical instability at its $Z$
$(0,0,1)$ point, which corresponds to the $A$ $(0,0,\frac{1}{2})$ point in the
parent $P6/mmm$ phase. Condensation of this instability leads to a
base-centered orthorhombic structure with the space group $Cmcm$ and $4Q$ order
parameter $M_1^+$ $(a,0,0)$ $+$ $L_2^-$ $(0,b,b)$ $+$ $A_6^+$
$(\frac{1}{2}c,\frac{-\sqrt{3}}{2}c)$.
