Common sugar alcohols used as artificial sweeteners and components of polymer networks represent low molecular weight polyhydroxymethylenes (PHMs) with the general formula [CH(OH)]n H2 but very low degree of polymerization (n = 2–6). Herein high molecular weight PHM (n >> 100) unparalleled in nature is tailored for 3D printing and medical applications by free radical polymerization of 1,3‐dioxol‐2‐one vinylene carbonate to produce polyvinylene carbonate (PVCA) which yields PHM by hydrolysis. Furthermore, PVCA is solution processable and enables PHM functionalization, membrane formation, and extrusion‐based 3D printing. Opposite to cellulose, amorphous PHM is plasticized by water and is readily functionalized via PVCA…