  We show that it is possible to confine light in a volume of order 10^-3 cubic
wavelengths using only dielectric material. Low-index (air) cavities are
simulated in high index rod-connected diamond (RCD) photonic crystals. These
cavities show long storage times (Q-factors >10^6) even at the lowest volumes.
Fabrication of such structures could open up a new field of photon level
interactions.
