Origami robots are well-suited for jumping maneuvers because of their light weight and ability to incorporate actuation and control strategies directly into the robot body. However, existing origami robots often model fold patterns as rigidly foldable and fail to take advantage of deformation in an origami sheet for potential energy storage. In this paper, we consider a parametric origami tessellation, the Reconfigurable Expanding Bistable Origami (REBO) pattern, which leverages face deformations to act as a nonlinear spring. We present a pseudo-rigid-body model for the REBO for computing its energy stored when compressed to a given displacement and compare that model to experimental measurements taken on a mechanical testing system. This stored potential energy, when released quickly, can cause the pattern to jump. Using our model and experimental data, we design and fabricate a jumping robot, REBOund, that uses the spring-like REBO pattern as its body. Four lightweight servo motors with custom release mechanisms allow for quick compression and release of the origami pattern, allowing the fold pattern to jump over its own height even when carrying 5 times its own weight in electronics and power. We further demonstrate that small geometric changes to the pattern allow us to change the jump height without changing the actuation or control mechanism.