We explored in situ a "directed" self-assembly of block copolymers into a twinned body-centered cubic sphere (bcc-sphere) with a special orientation via the order-order phase transition from a specially aligned hexagonal cylinder (hex-cyl) by using time-resolved synchrotron small-angle X-ray scattering and transmission electron microscopy. We elucidated that the hex-cyl with its cylinder axis and {11} lattice plane aligned respectively parallel to the OX axis and the OXZ plane was epitaxially transformed into the twin bcc-sphere with its twin axis < 111 > and twin plane {112} having respectively the "directed orientation" parallel to the OX axis and the OXZ plane. We found that the directed self-assembly involves a three-step nucleation growth (NG) process as follows. Step I corresponds to a pretransition process, where hex-cyl undergoes the cooperative and periodic undulation of the cylinders with their pinching or bulging points being spatially arranged with the "bcc symmetry" which is attained in bcc-sphere after completion of the transformation (designated as "undulated hex-cyl"). Moreover, the undulation fluctuations modes found to have the degeneracy in the form of the undulations with bcc-symmetry A and those with bcc-symmetry A' which have the twin relationship to each other. Step II involves NG of two types of bcc-sphere (designated as A- and A'-sphere which have a mirror symmetry with respect to the {112} plane parallel to the OXZ plane) formed with an equal statistical weight in the matrix of the undulated hex-cylinder; Grains of bcc-sphere grow at the expense of the matrix phase at a faster growth rate parallel to < 111 > axis than normal to it. Step III involves impingements of bcc-sphere A and A' with their twin planes {112} as their grain boundaries and with their twin axes < 111 > parallel to the OXZ plane and the OX axis, respectively. Thus, the volume-filling A- and A'-spheres accompanied by spatial rearrangements toward a more perfect bcc-sphere are inevitably directed to form twin bcc-sphere composed of bcc-sphere A and A'.