The Platonic Solids: a Three-Dimensional Textbook is an exhibit in the 2015 Bridges conference that includes geometric sculptures, depicting the geometric relationships between the five Platonic solids, as well as extensive text explaining and developing those geometric ideas. The Platonic solids serve as a very accessible vehicle for introducing ideas from projective geometry and group theory. It is fitting to depict beautiful mathematical ideas with beautifully crafted models. It is hoped that others will in the future be inspired to make “three-dimensional textbooks” for other topics in geometry.