More generally yet: Let A={a_j} and B={b_j} be sets of N points in R^a and R^b, respectively, and ask whether there is a set X of points in R^n, n < a + b, and subspaces P = R^a and Q = R^b of R^n such that the orthogonal projections of X onto P and Q are congruent to A and B, respectively. ----- *This* is the possibly interesting question: ----- Given two sets A and B of N points in R^2, when is there a set X in R^3 and 2-planes P, Q in R^3 with the orthogonal projections of X onto P, Q having images congruent to A and B, respectively? More generally, replace R^2 with R^k, and R^3 with R^n for n < 2k. ----- E.g.: ----- Given any two triangles T_1, T_2, when does there exist a set X of size 3 in R^3, and two 2-planes P_1, P_2 in R^3 with the orthogonal projection of X onto P_j congruent to T_j ??? —Dan