Many students at all levels--from middle school to graduate programs for in-service teachers--struggle with visualizing three-dimensional shapes. Many also are challenged to locate appropriate centers of rotation, placement of lines of symmetry, and translation vectors for transformations on the plane. Hands-on experience helps with these concepts. Using these concepts to construct a satisfying result, rather than simply completing an out-of-context exercise, is a powerful motivator. Collapsible models of polyhedra that students can build and tuck into their textbooks for future reference as they do assignments can be useful manipulatives. In this article, the author describes her use of polyhedra, pop-up polyhedra, and The Geometer's Sketchpad[R] (GSP) as tools to explore transformations in the plane and three-dimensional models. This activity has been adapted for use with in-service teachers at a regional conference, preservice teachers in the classroom, and middle school students in special conference settings, and it has been part of a lecture demonstration using a computer station with students completing constructions independently outside class. Its most successful implementation has been in a computer laboratory in which individual students have their own stations, the teacher has a display station, and a printer is readily available to print results for immediate three-dimensional construction. This article provides suggestions for construction of the Platonic solids, but it also opens the door to creative construction of the Archimedean solids and other solids that do not appear in the pop-up literature. (Contains 10 figures and 3 resources.)