Synergetic chemomechanical oscillators represent a fundamentally new class of oscillators, where a clock reaction, owning no oscillatory chemical kinetics, generates shrinking-swelling cycles in a chemoresponsive gel under appropriate fixed nonequilibrium boundary conditions. Sufficiently large size-changes are a condition for continually switching between a reacted and an unreacted chemical state in the gel through sufficiently large differences in the diffusion time between the environment and the core of the gel. Two former experimental demonstrations with acid autocatalytic reactions were frustrated either by complex behaviors (chlorite-tetrathionate system) or by side reactions with the gel matrix (bromate-sulfite system). With the Landolt (iodate-sulfite) reaction, regular large-amplitude chemomechanical oscillations can be sustained for more than a week. This enabled a fine study of the temperature and stoichiometry range of operation. I have identified several key steps that are experimentally essential to the systematic design of further synergetic oscillators. The robust realization of this type of self-organization in artificial systems is currently unique.