On the number of components of a three-dimensional maximal intersection of three real quadrics

We consider non-singular intersections of three real five-dimensional quadrics. For brevity they are referred to as real three-dimensional triquadrics. We prove the existence of real three-dimensional $M$-triquadrics with $k$ components, where $k$ is any integer in the range $1\leqslant k\leqslant 14$.