I have read in a couple of sources that a graph with n vertices is rigid in d dimensions if and only if its rigidity matroid has rank nd - d(d+1)/2. C3 (a triangle graph) has a rigidity matroid of rank 3 for all dimensions greater than 1 (3 is an upper bound, because the rigidity matrix only has 3 rows, and this bound is already realized for d = 2).
Since 3 > 3*d-d*(d+1)/2 for d > 3, this suggests that C3 becomes flexible in 4 and higher dimensions. However, since C3 is a complete graph, the distances between vertices cannot change, so it should be rigid for all d.
Can someone clear up this conundrum?