= Solution
For a finite nonempty collection $X=\{p_1,\ldots,p_n\}\subset\mathbb R^3$, its <convex hull> is the smallest <convex set> containing all the <points>. Equivalently, it is the <set> of all <convex combinations>:
$$
\boxed{\operatorname{conv}X=
\left\{\sum_{i=1}^n\lambda_ip_i:\lambda_i\ge0,\ \sum_{i=1}^n\lambda_i=1\right\}.}
$$
Every <convex set> containing the $p_i$ must contain these combinations; the displayed <set> is itself <convex> and contains each $p_i$, proving the equivalence. For a full-dimensional finite collection this is a <convex polyhedron>. A collinear or coplanar collection instead has a lower-dimensional <convex hull>, so the solid case needs a separate dimensionality assumption.
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