Existing protein geometry models usually describe molecular surfaces with local geometric features such as sampled points, normals, and curvature. While these representations capture the exposed shape, they do not explicitly model the volumetric organization beneath the surface nor provide a consistent coordinate system for residue‑wise volumetric structure.\ \ We introduce Protein‑TetSphere, a registered residue‑wise volumetric representation. Each protein chain is tetrahedralized to obtain local volumetric regions associated with individual residues. These regions are then registered to a shared fixed‑topology tetrahedral reference and expressed in a common Laplacian basis. This registration yields consistent volumetric coordinates across residues, allowing local three‑dimensional deformation to be integrated with surface and chemical information in a multimodal protein representation.\ \ We evaluate Protein‑TetSphere on three tasks: ligand‑binding pocket classification, protein‑protein interface prediction, and de novo protein binder design. Results show that pocket balanced accuracy improves from $0.795$ to $0.826$; Pinder‑Pair/Site AUROC rises from $0.914/0.852$ to $0.932/0.866$; binder‑design success increases from $14.95\%$ to $19.90\%$ on the BoltzGen Challenge Set and from $27.62\%$ to $32.19\%$ at the ProtDBench backbone level. These findings demonstrate that registered volumetric geometry supplies complementary spatial information beyond molecular surfaces, enhancing protein recognition, interaction, and design.\ \ Review