A reciprocal 360-degree three-dimensional light-field image acquisition and display system was designed using a common catadioptric optical configuration and a lens array. Proof-of-concept experimental setups were constructed with a full capturing part and a truncated display section to demonstrate that the proposed design works without loss of generality. Unlike conventional setups, which record and display rectangular volumes, the proposed configuration records 3D images from its surrounding spherical volume in the capture mode and project 3D images to the same spherical volume in the display mode. This is particularly advantageous in comparison to other 360-degree multi-camera and multiple projector display systems which require extensive image and physical calibration. We analysed the system and showed the quality measures such as angular resolution and space bandwidth product based on design parameters. The issue due to the pixel size difference between the available imaging sensor and the display was also addressed. A diffractive microlens array matching the sensor size is used in the acquisition part whereas a vacuum cast lens array matching the display size is used in the display part with scaled optics. The experimental results demonstrate the proposed system design works well and in good agreement with the simulation results.