Boolean operations between solids can be efficiently performed by operating their respective octree encodings. Among the variety of octree-based representation models, face octrees are approximate representations that give a good compromise between the need of storage saving and the simplicity of the involved algorithms. They are also a valuable model for representing smooth free-form surfaces. Constructing face octrees from voxel-based volumes representations will be useful in order to obtain a more compact, smoother, and further operable encoding. A method to perform such a conversion is presented. The method consists of two steps. First, a network of points that represents the volume data is extracted. The extraction is based on the Geometrically Deformed Models technique. Then the network of points is transformed into a face octree. In the transformation process, face octree nodes are compacted as much as possible while preserving the volume data precision.