A precise and accurate measurement of the crystal structure of ice-Ih is hindered by its disordered H-bond network. In this work, we carried out first-principle calculations to study the effects of H-bond topology on the structure of ice-Ih with emphasis on the molecular geometry of water and the distortion in oxygen lattice. An analytic algorithm based on group and graph theory is employed to enumerate all possible configurations in a given unit cell and to select a set of structures for detailed examinations. In total we have studied more than 60 ice-Ih structures in a hexagonal unit cell of 48 water molecules by quantum-chemical methods and found a significant amount of static distortion in the oxygen positions from their crystallographic positions which is in good agreements with highly significant higher-order terms obtained from both x-ray and neutron-diffraction data. Much debated structural information such as H-O-H angle and O-H bond length is found to be 106.34+/-0.36 degrees and 0.9997+/-0.0008 A, compared to experimental value of 106.6+/-1.5 degrees and 0.986+/-0.005 A. Detailed benchmarking calculations were carried out to gauge the influence of using different exchange and correlation functionals, pseudopotentials, and unit-cell sizes. Our results have proven that first-principle methods are useful complementary tools to experiments, especially for cases in which experimental accuracy is limited by intrinsic orientational disorder.