  Stimulated by the observation of the $X(6900)$ from LHCb in 2020 and the
recent results from CMS and ATLAS in the di-$J/\psi$ invariant mass spectrum,
in this work we systemically study all possible configurations for the ground
fully heavy tetraquark states in constituent quark model. By our calculation,
we present their spectroscopy behaviors like binding energy, lowest meson-meson
thresholds, specific wave function, magnetic moment, transition magnetic
moment, radiative decay width, rearrangement strong width ratio, internal mass
contributions, relative lengths between (anti)quarks, and the spatial
distribution of four valence (anti)quarks. We cannot find stable S-wave state
for the fully heavy tetraquark system. We hope that our results are valuable to
further explore fully heavy tetraquark states in experiment.
