Thanks to the Multidimansional Szemerédi Theorem one can find any constelation in the stars.

The Multidimensional Szemerédi Theorem: Let E ⊆ Z^m of positive upper density; i.e. limsup |E ∩ [-N,N] ^m|/ | (2N)^m| > δ, and let K be a finite subset of Z^m . Then E contains a dilated shift of K, namely there exist and integer n, and a v &isin Z^m; , such that v+nK ∈ E.

This theorem was first proved by Furstenberg and Katznelson in 1978 using ergodic theoretic methods. It was later given a combinatorial proof by Gowers and independently by Rodl, Schacht, Tengan and Tokushige. Another proof was given by Tao .