The possibility to align and organize faceted particles in the bulk offers intriguing possibilities for the design and discovery of materials and architectures exhibiting novel functional properties. The growth of ice crystals can be used to trigger the self-assembly of large, anisotropic particles and consequently to obtain three-dimensional porous materials of large dimensions in a limited amount of time. These mechanisms have not been explored so far due to the difficulty to experimentally investigate these systems. Here we elucidate the self-assembly mechanisms of faceted particles driven by ice growth by a combination of X-ray holotomography and discrete element modeling, providing insights into both the dynamics of self-assembly and their final packing. The encapsulation of particles is the result of a delicate balance between the force exerted by the percolating network of concentrated particles and the force exerted by the moving interface. We illustrate the benefits of such self-assembly for thermal management composite materials.