  To-date, despite remarkable applications in optoelectronics and tremendous
amount of theoretical, computational and experimental efforts, there is no
technological pathway enabling the fabrication of 3D photonic band gaps in the
visible range. The resolution of advanced 3D printing technology does not allow
to fabricate such materials and the current silica-based nanofabrication
approaches do not permit the structuring of the desired optical material.
Materials based on colloidal self-assembly of polymer spheres open 3D complete
band gaps in the infrared range, but, owing to their critical index, not in the
visible range. More complex systems, based on oriented tetrahedrons, are still
prospected. Here we show, numerically, that FCC foams (Kepler structure) open a
3D complete band gap with a critical index of 2.80, thus compatible with the
use of rutile TiO2. We produce monodisperse solid Kepler foams including
thousands of pores, down to 10 um, and present a technological pathway, based
on standard technologies, enabling the downsizing of such foams down to 400 nm,
a size enabling the opening of a complete band gap centered at 500 nm.
