This research investigates the geometric procedures of 3D Graphic Statics using reciprocal polyhedral diagrams. The concentration is in the procedural construction of the reciprocal form and force diagrams in polyhedral space. The design and analysis methods developed in this research are equivalent to the existing methods of 2D Graphic Statics; it includes the topics such as constrained form finding, funicular polyhedral construction, etc.Triskeles bridge is a conceptual design of a funicular spatial bridge that spans over three support locations in Lauterbrunnen, Switzerland. The structural form of this bridge is derived using 3D Graphic Statics method using reciprocal polyhedral diagrams. The largest span of the bridge is 150 m. The bridge has a depth of 12 m in its deepest part. The funicular form and force diagrams constrained to three support locations include compression (blue spectrum) and tensile members (red). Note that the original form and force diagrams include additional tensile members connecting three supports. reducing these elements from the geometry of form requires additional pre-stressing force to be applied at the supports to guarantee the equilibrium.