We consider the problem of reconstructing a graph G from a query Q which, for every k-subset of vertices S, provides some information Q(G)(S) about the induced subgraph G[S]. The vertices are labelled from 1 to n, so reconstruction up to isomorphism is not sufficient, we need to know which label is where. We have studied the case k=3. Given a query Q on triples, we are interested in two things: a structural characterization of all graphs G that are uniquely reconstructible from the function Q(G) (i.e. such that Q(H)=Q(G) if and only if H=G), and a polynomial-delay enumeration algorithm of all graphs that are consistent with some input query answers. In 2023, Qi and Bastide et al. respectively have managed this for the connectivity query (meaning that, for every triple S, Q(G)(S) indicates whether G[S] is connected). We have obtained the same results for all 13 other non-trivial queries on triples. This presentation will go into details of a select few of these queries. Joint work with Hoang La, Raphaëlle Maistre, Matthieu Petiteau and Dimitri Watel.