We demonstrate a volumetric mesh-based mapping of the placenta to a canonical template that resembles the better-known ex vivo shape. Placental shape presents significant challenges for visualization of the associated signals. No standard framework exists for visualizing the organ in vivo. Our approach is to flatten a volumetric mesh that captures subject-specific placental shape while penalizing local distortion to maintain anatomical fidelity. The resulting algorithm produces an invertible transformation to the canonical template. To demonstrate the promise of the proposed approach, we present visualization of BOLD MRI intensity and oxygenation measures after mapping them to a flattened placenta template.