The shape of the triiodide ion $\mathrm{I}{}_3{}^{-}$ is

Central I has 7 valence electrons, plus 2 from the bonded I atoms and 1 for the charge, i.e. 10 electrons = 5 pairs. Two pairs are bond pairs and three are lone pairs ($s{p}^{3}d$), the lone pairs sit in the equatorial plane, so the ion is linear.