Trends in the aerospace industry are driving payloads to be smaller and less expensive while yet delivering comparatively large antennas. Deployable reflectarray antennas are often used to meet these demands. The more that a deployable reflectarray fills an allotted volume in the stowed state, the greater the surface area it will realize in the deployed state. Thick, flat-foldable origami designs are therefore excellent design candidates for reflectarray antennas, as they stow as efficiently as possible. This is desirable for antennas as surface area is directly proportional to gain. Gain is also affected by efficiency, which is a function of the geometry of the antenna aperture. As the most efficient rectangular reflectarray profile is a square, this work develops the metrics and relationships that enable an optimization problem seeking to maximize surface area subject to the constraints of an allotted cuboid volume and a deployed aspect ratio of one. The source origami is a modified thickness-accommodating Miura-ori pattern herein termed volume-efficient Miura-ori (VEMO), selected for its ability to fold into a rectangular profile and easily adapt to different aspect ratios. A case study is presented with an allotted 1U CubeSat volume and a panel thickness of 2.5 mm.