# algorithm of polytope

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.

• It seems to me that, a priori, there is absolutely no relation between $F_i$ and $V_{i-1}$. It may happen that $V_{i-1}$ is entirely in the interior of $P_i$. – Alex Degtyarev Mar 22 '15 at 21:56
• well, it would make sense to add vertices one by one... – Dima Pasechnik Mar 22 '15 at 22:11