The structural performance of cellular polyhedral funicular geometries in 3D graphic statics(3DGS) relies heavily on the buckling performance of the system; if the edges of the form diagram are immediately translated to structural members. Besides, the spatial geometry of the nodes makes the fabrication process quite challenging. This research proposes a novel approach to translate a polyhedral cellular geometry into a polyhedral surface-based structure in 3DGS that is comparable to the widely known minimal surface geometries in the context of structural design, bridging the gap between polyhedral cellular geometry and surface-based structure. Using such anti-clastic structures for materialization in place of polyhedral geometries in 3DGS improves the structural performance of the system and facilitates its fabrications process. The proposed approach introduces a new typology of funicular spatial structures consist of a minimal surface for a given boundary condition. Numerous studies show that the high surface-to-volume ratio in minimal surface geometries enhances mechanical performance. In this research, we are trying to get as close as possible to such geometries utilizing 3D graphic statics to take advantage of their properties in many fields such as architectural design, structural design, biomechanics, biochemistry, and beyond.