We report on the fabrication of inverted Yablonovite-like three-dimensional photonic crystals by nonlinear optical nanolithography based on two-photon polymerization of a zirconium propoxide hybrid organic-inorganic material with Irgacure 369 as photo-initiator. Advantage of this material is ultra-low shrinkage that guaranty high fabrication fidelity. Images of the fabricated structure are obtained with a scanning electron microscope. The photonic crystal consists of three sets of nearly cylindrical structural elements directed along the three lattice vectors of the fcc lattice and cross each other at certain angles to produce inverted Yablonovite geometry. To investigate photonic properties of the inverted Yablonovite structures, we calculate the photonic band structure for ten lowest-frequency electromagnetic modes. In contrast to the direct Yablonovite structure that has a complete photonic band gap between the second and third bands, we find no complete photonic band gaps in the inverted Yablonovite lattice. This situation is opposite to the case of fcc lattice of close-packed dielectric spheres in air that has a complete photonic band gap only for the inverted geometry.