Hexagonally ordered spherical and cylindrical morphologies (P(6)/mmm and P(6)/mm space group symmetries) have been identified in bulk poly(styrene-b-isoprene-b-styrene-b-ethylene oxide) (SISO) tetrablock terpolymers. These materials were synthesized by adding up to 32% by volume O blocks to a parent hydroxy-terminated SIS triblock copolymer containing 40% S by volume, and the resulting morphologies were characterized by small-angle X-ray scattering, transmission electron microscopy, differential scanning calorimetry and dynamic mechanical spectroscopy. Disordered, spherical and cylindrical phases were documented with increasino content, where both ordered states exhibit hexagonal symmetry. Theoretical calculations based on a numerical self-consistent field theory for polymers provide crucial insights into the molecular configurations associated with these morphologies. These results offer a new approach to independently control domain shape and packing in block copolymer melts through manipulation of the magnitude and sequencing of the binary segment segment interactions (chi(SI) <= chi(SO) <= chi(IO)), which dictate core segregation and the effective interdomain interactions.