  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.
