© 2022 ACM.This study introduces Co-gnito, a participatory physicalization game that supports collaborative urban mental mapping through storytelling. Through Co-gnito we investigate gaming as a means to elicit subjective spatial experiences and to steer the synchronous construction of a physicalization that aligns and represents them. Co-gnito was evaluated during seven deployments by analyzing how 28 players mapped their spatial experiences of two university campuses. Our results indicate that storytelling as a gaming mechanic, guided and motivated the gradual addition of personal contributions towards a collective outcome, but its reward system did not nudge the mapping direction as expected. We also demonstrate how the shared construction process of a physicalization is influenced by how the data encoding scheme was negotiated, by the token physical affordances and by the game mechanics. We therefore believe that our core contributions, comprising of: 1) a working research prototype; 2) an augmentation of the physicalization pipeline towards collaborative settings; and 3) a set of reflective considerations, provide actionable knowledge on how to design participatory physicalizations in the future.