We propose systems with structures defined by self-assembled triply periodic minimal surfaces (STPMS) as candidates for photonic bandgap materials. To support our proposal we have calculated the photonic bands for different STPMS and we have found that, at least, the double diamond and gyroid structures present full photonic bandgaps. Given the great variety of systems which crystalize in these structures, the diversity of possible materials that form them and the range of lattice constants they present, the construction of photonic bandgap materials with gaps in the visible range may be presently within reach.
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