This work evaluates a specific origami device known as the kaleidocycle and the broad classof rigidly foldable origami. Both of these have potential for application in the design of deployableand foldable arrays of spatial mechanisms.Origami is considered a compliant mechanisms because it achieves its motion through thedeflection of paper creases. Compliant mechanisms generally do not allow for continuous rotation;however, the compliant kaleidocycle represents an exception to this generality. Along with theirability to rotate continuously, kaleidocycles may also be designed to exhibit multistable behaviorduring this rotation. These two characteristics make the kaleidocycle an interesting device withpotential for applications in engineering. This work presents the multistable characteristics ofkaleidocycles, showing that devices can be made which exhibit one, two, three, or four distinctstable equilibrium positions. Kaleiocycles may also be designed to exhibit a range over which thedevice is neutrally stable.The second type of origami presented in this work is rigidly foldable origami, a special classof origami in which all deflection occurs at the creases, allowing the panels to remain rigid. Thistype of origami is of particular interest because of its ability to be constructed from materials muchstiffer than paper while retaining its mobility. This property allows rigidly foldable origami to beapplied to fields such as architecture and deployable mechanisms. This work presents a method forevaluating rigid foldability in origami tessellations. This method is used to define seven theoremsfor the rigid foldability of origami twists and to develop new rigidly foldable origami “gadgets”and tessellations.