A finfish aquaculture containment pen having a plurality of panels that when joined together form the majority of the exterior surface of the containment pen. The panels each comprise tension-bearing mesh material forming the exterior surface of the containment pen, a plurality of compression-bearing struts extending along the boundaries between panels, wherein the mesh material is attached to the struts along the lengths of the struts, and a plurality of hubs at which a plurality of struts and the corners of a plurality of panels abut each other. The panels can form a polyhedral structure. The mesh can comprise coated wire mesh. The struts can be curved members with convex curvature.