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Shape displays are a class of haptic devices that enable whole-hand haptic exploration of 3D surfaces. However, their scalability is limited by the mechanical complexity and high cost of traditional actuator arrays. In this paper, we propose using electroadhesive auxetic skins as a strain-limiting layer to create programmable shape change in a continuous (“formable crust”) shape display. Auxetic skins are manufactured as flexible printed circuit boards with dielectric-laminated electrodes on each auxetic unit cell (AUC), using monolithic fabrication to lower cost and assembly time. By layering multiple sheets and applying a voltage between electrodes on subsequent layers, electroadhesion locks individual AUCs, achieving a maximum in-plane stiffness variation of 7.6x with a power consumption of 50 μW/AUC. We first characterize an individual AUC and compare results to a kinematic model. We then validate the ability of a 5x5 AUC array to actively modify its own axial and transverse stiffness. Finally, we demonstrate this array in a continuous shape display as a strain-limiting skin to programmatically modulate the shape output of an inflatable LDPE pouch. Integrating electroadhesion with auxetics enables new capabilities for scalable, low-profile, and low-power control of flexible robotic systems.