Basically, we have an incremental sets of vertices

$${V_1} \subset {V_2} \subset ...$$

for each of them, we could build a polytope $${P_i} = Conv({V_i})$$

Consequently, we can compute

$${F_i} = Facet\left( {{P_i}} \right)$$

So my question is, what is the best numerical procedures to compute such $F_i$ from given ${V_1} \subset {V_2} \subset ...$ ? Thank you.