We report on an experiment conducted with pre-service teachers in France and in Quebec. They were submitted to a classroom situation involving regular polyhedra. We expected that through the activities of defining, of exploring and experimenting via concrete constructions and manipulation, students would reflect on the link face angle – dihedral angle and would eventually be led to the proof that there exist only five regular polyhedra. We witnessed instead how experimentation and construction, in conjunction with students’ uncontrolled tendencies to resort to intuition and analogy, contributed to movements away from relevant reasoning and proving activities. We offer hypotheses of causes and discuss possible remediations in the conclusion.