Demospongiae is a class of marine sponges that mineralize skeletal elements, the glass spicules, made of amorphous silica. The spicules exhibit a diversity of highly regular three-dimensional branched morphologies that are a paradigm example of symmetry in biological systems. Current glass shaping technology requires treatment at high temperatures. In this context, the mechanism by which glass architectures are formed by living organisms remains a mystery. We uncover the principles of spicule morphogenesis. During spicule formation, the process of silica deposition is templated by an organic filament. It is composed of enzymatically active proteins arranged in a mesoscopic hexagonal crystal-like structure. In analogy to synthetic inorganic nanocrystals that show high spatial regularity, we demonstrate that the branching of the filament follows specific crystallographic directions of the protein lattice. In correlation with the symmetry of the lattice, filament branching determines the highly regular morphology of the spicules on the macroscale.