Reciprocal Frames (RF) are a type of structural system that can be used to build temporary structures with large spans. This is possible due their ease of assembly and the use of relatively short, light-weight elements. However, a challenge is presented when this kind of structure is applied to complex surfaces. In this case, the only way to figure out each connection is through an algorithmic geometric model. Only a few algorithms have already been developed for generating complex RF structures, but they still have some limitations. In this paper we present a new approach represent RF geometry, based on symmetry theory, combining pinwheel patterns with wallpaper symmetry groups. In future works, this will be combined with structural performance analysis and the use of digital fabrication methods for producing the structures’ connections.

互易框架 (RF) 是一种结构系统，可用于建造大跨度的临时结构。这是可能的，因为它们易于组装并使用相对较短、重量较轻的元件。然而，当这种结构应用于复杂的表面时，就会出现一个挑战。在这种情况下，找出每个连接的唯一方法是通过算法几何模型。目前只有少数算法被开发用于生成复杂的射频结构，但它们仍然存在一些局限性。在本文中，我们提出了一种基于对称理论的表示 RF 几何的新方法，将风车图案与壁纸对称群相结合。在未来的工作中，这将结合结构性能分析和使用数字制造方法来产生结构的连接。