A Physical Proof for Five and Only Five Regular Solids

Robert McDermott
Renaissance Banff: Mathematics, Music, Art, Culture (2005)
Pages 523–528


Physical models are invaluable aids for conveying concepts in geometry, particularly concepts about polyhedra. In this paper physical polygons, polygon corners, polygon flat regions, polygon cylinders, polygon nets and polyhedra are all used to show a physical proof that there are five, and only five regular solids. Students from grade school, high school, undergraduate and graduate levels have been presented with this physical proof, and all of them have taken away something worthwhile related to their existing level of knowledge.