  In this article, we construct the axialvector-diquark-axialvector-antidiquark
type currents to study both the vector and axialvector $QQ\bar{Q}\bar{Q}$
tetraquark states with the QCD sum rules, and obtain the masses
$M_{Y(cc\bar{c}\bar{c},1^{+-})} =6.05\pm0.08\,\rm{GeV}$,
$M_{Y(cc\bar{c}\bar{c},1^{--})} =6.11\pm0.08\,\rm{GeV}$,
$M_{Y(bb\bar{b}\bar{b},1^{+-})} =18.84\pm0.09\,\rm{GeV}$,
$M_{Y(bb\bar{b}\bar{b},1^{--})} =18.89\pm0.09\,\rm{GeV}$. The vector tetraquark
states lie $40\,\rm{MeV}$ above the corresponding centroids of the $0^{++}$,
$1^{+-}$ and $2^{++}$ tetraquark states, which is a typical feature of the
vector tetraquark states consist of four heavy quarks.
