The synthesis, molecular and morphological characterization of a 3-miktoarm star terpolymer of polystyrene (PS, Mn = 61.0 kg/mol), polybutadiene (PB, Mn = 38.2 kg/mol) and polyisoprene (PI, Mn = 29.2 kg/mol), corresponding to volume fractions (φ) of 0.46, 0.31 and 0.23 respectively, was studied. The major difference of the present material from previous ABC miktoarm stars (which is a star architecture bearing three different segments, all connected to a single junction point) with the same block components is the high 3,4-microstructure (55%) of the PI chains. The interaction parameter and the degree of polymerization of the two polydienes is sufficiently positive to create a three-phase microdomain structure as evidenced by differential scanning calorimetry and transmission electron microscopy (TEM). These results in combination with small-angle X-ray scattering (SAXS) and birefringence experiments suggest a cubic tricontinuous network structure, based on the I4132 space group never reported previously for such an architecture.