Explicit models of ℓ_1-preduals and the weak* fixed point property in ℓ_1

. We provide a concrete isometric description of all the preduals of P1 for which the standard basis in P1 has a finite number of w*-limit points. Then, we apply this result to give an example of an P1-predual X such that its dual X* lacks the weak* fixed point property for nonexpansive mappings (briefly, w*-FPP), but X does not contain an isometric copy of any hyperplane W alpha of the space c of convergent sequences such that W alpha is a predual of P1 and W alpha* lacks the w*-FPP. This answers a question left open in the 2017 paper of the present authors.