5 kinds of regular polyhedra and 13 kinds of semi-regular polyhedra are taken as the main research objects in this paper to explore the form design method of polyhedral expansion through the rotation of polygon. Firstly, the expandable range of uniform convex polyhedra is defined and divided into two types of expansion. Then three solutions are proposed, namely, discarding polygonal faces, constructing rigid-foldable origami mechanisms and constructing scissor-like elements, so that the prior unexpandable uniform convex polyhedron can be expanded. These methods extend the range of expandable uniform convex polyhedron, and can provide new form design ideas for frontier fields such as movable furniture (toys), movable art installations, 3D kinetic facades and space architecture.
Uniform convex polyhedra; Expansion; Movable structures; Form design
