2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/219303Equation of state parameter plays a significant role for guessing the real nature of dark energy. In the present paper polytropic equation of state $p=ωρ^n$ is chosen for some of the kinematical $Λ$-models viz., $Λ\sim (\dot a/a)^2$, $Λ\sim \ddot a/a$ and $Λ\sim ρ$. Although in dust cases ($ω=0$) closed form solutions show no dependency on the polytropic index $n$, but in non-dust situations some new possibilities are opened up including phantom energy with supernegative ($ω<-1$) equation of state parameter.Latex, 6 pagesAstrophysicstext