Experimental procedures. Schematic representation of the procedures used in Experiment 1, 2 and 3. The first and second experiment employed a social cued memory procedure (spontaneous approaches), while the third experiment employed a reference memory procedure (training over time). In details, Experiment 1 consisted of three periods: “observation” (120 seconds), where the fish was placed in a glass jar in the centre of the arena and could observe the social cue placed in a glass jar at a correct corner; “disorientation procedure” (30 seconds), where the fish was taken out from the arena and slowly rotate 360° clockwise/counter-clockwise, while the jar containing the social cue was replaced with a water-filled jar; “test” (120 seconds), where the fish was reinserted in the centre of the arena, free to approach the four jars placed at corners. Under such conditions, fish could not explore the arena to gain experience, but only observe the social cue. Experiment 2 was performed similarly but introducing two different periods before disorientation and test, that were “acclimation” (30 seconds), where the fish was placed in a glass jar in the centre of the arena and could accustom to the environment, and “exploration” (120 seconds), where the fish could swim in the arena and experience its shape in relation to the social goal for a short period through extra-visual modalities as, for instance, the lateral line and/or the sense of touch. Experiment 3 allowed fish to protractedly experience the rectangular environment and consisted of two phases: “training”, where the fish was trained to choose two geometrically equivalent corners (here indicated with “+”) to get a reward (food, conspecifics and prolonged inter-trial breaks), until reaching a learning criterion greater or equal to 70% of correct choices for two consecutive days of training; “geometric test”, in extinction of response (all corridors were closed; here indicated with “−”), with the aim to bear out that the learning had been achieved on geometric cues. Before each trial fish underwent the disorientation procedure (as done in Experiment 1 and 2), in order to reduce the use of compass and inertial information.