We have investigated the crystal structure of Ca(BD4)(2) by combined synchrotron radiation X-ray powder diffraction, neutron powder diffraction, and ab initio calculations. Ca(BD4)(2) shows a variety of structures depending on the synthesis and temperature of the samples. An unknown tetragonal crystal of Ca(BD4)(2), the phase has been solved from diffraction data measured at 480 K on a sample synthesized by solid-gas mechanochemical reaction by using MgB2 as starting material. Above 400 K, this sample has the particularity to be almost completely into the beta phase of Ca(BD4)(2). Seven tetragonal structure candidates gave similar fit of the experimental data. However, combined experimental and ab initio calculations have shown that the best description of the structure is with the space group P4(2)/m based on appropriate size/geometry of the (BD4) tetrahedra, the lowest calculated formation energy, and real positive vibrational energy, indicating a stable structure. At room temperature, this sample consists mainly of the previously reported alpha phase with space group Fddd. In the diffraction data, we have identified weak peaks of a hitherto unsolved structure of an orthorombic gamma phase of Ca(BD4)(2). To properly fit the diffraction data used to solve and refine the structure of the beta phase, a preliminar structural model of the gamma phase was used. A second set of diffraction data on a sample synthesized by wet chemical method, where the gamma phase is present in significant amount, allowed us to index this phase and determine the preliminar model with space group Pbca. Ab initio calculations provide formation energies of the alpha phase and beta phase of the same order of magnitude (Delta H <= 0.15 eV). This indicates the possibility of coexistence of these phases at the same thermodynamical conditions.