A dodecagonal quasicrystalline (QC) morphology is identified in a poly(styrene-b-isoprene-b-styrene-b-ethylene oxide) (SISO) tetrablock terpolymer based on evidence provided by transmission electron microscopy (TEM), small-angle X-ray scattering, and dynamic mechanical spectroscopy measurements. The QC state occurs at temperatures between those associated with simple hexagonal order (HEX) and the σ-phase (P4 2/mnm), T HEX < T QC < T σ < T ODT, where T ODT is the order-disorder transition temperature. All three morphologies are formed from spherical domains containing an O core surrounded by a shell of S that screens unfavorable segment-segment interactions with an I-rich matrix. TEM analysis reveals a QC morphology with 12-fold rotational symmetry but devoid of long-range translational order, along with locally coordinated structures consistent with dodecagonal quasicrystalline approximants. The SISO molecular architecture decouples control over the domain shape and interdomain interactions, leading to a multiplicity of packing symmetries.