We study the six diagrams generated by the first three Schechter interpolators \(\Delta _2(f)= f''(1/2)/2!, \Delta _1(f)= f'(1/2), \Delta _0(f)=f(1/2)\) acting on the Calderón space associated to the pair \((\ell _\infty , \ell _1)\) . We will study the remarkable and somehow unexpected properties of all the spaces appearing in those diagrams: two new spaces (and their duals), two Orlicz spaces (and their duals) in addition to the third order Rochberg space, the standard Kalton-Peck space \(Z_2\) and, of course, the Hilbert space \(\ell _2\) . We will also deal with a nice test case: that of weighted \(\ell _2\) spaces, in which case all involved spaces are Hilbert spaces.
