Fully strange tetraquark <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>s</mml:mi><mml:mi>s</mml:mi><mml:mover accent="true"><mml:mi>s</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mover accent="true"><mml:mi>s</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover></mml:math> spectrum and possible experimental evidence

In this work, we construct 36 tetraquark configurations for the $1S$-, $1P$-, and $2S$-wave states, make a prediction of mass spectrum $ss\overline{s}\overline{s}$ system in framework nonrelativistic potential quark model without diquark-antidiquark approximation. The parameters are well determined by our previous study strangeonium spectrum. We find that resonances ${f}_{0}(2200)$ ${f}_{2}(2340)$ may favor assignments ground states ${T}_{(ss\overline{s}\overline{s}){0}^{++}}(2218)$ ${T}_{(ss\overline{s}\overline{s}){2}^{++}}(2378)$, respectively, newly observed $X(2500)$ at BESIII be candidate lowest $1P$-wave ${0}^{\ensuremath{-}+}$ state ${T}_{(ss\overline{s}\overline{s}){0}^{\ensuremath{-}+}}(2481)$. Signals other ${0}^{++}$ ${T}_{(ss\overline{s}\overline{s}){0}^{++}}(2440)$ also have been $\ensuremath{\phi}\ensuremath{\phi}$ invariant $J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\phi}\ensuremath{\phi}$ BESIII. masses ${J}^{PC}={1}^{\ensuremath{-}\ensuremath{-}}$ ${T}_{ss\overline{s}\overline{s}}$ predicted to range $\ensuremath{\sim}2.44--2.99\text{ }\text{ }\mathrm{GeV}$, which indicates $\ensuremath{\phi}(2170)$ resonance not good state. This provide useful guidance searching experiments.