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This paper deals with the use of reciprocal frames in temporary gridshell structures, such as architectural pavilions in expositions and installations. These architectural examples can benefit from the use of short, easy to handle, generally joint-free, and repeatable “modules” in order to create particular self-supporting structures. The lightweight and interwoven grid obtained by connecting short elements according to the reciprocity principle is structurally efficient and, at the same time, aesthetically pleasing, mainly due to the resulting tessellation. The paper firstly investigates the connection between efficiency and aesthetics. The last part of the paper investigates some temporary architectural pavilions from both an aesthetical and parametric point of view. In order to deepen our understanding of these structures, they are re-modelled according to a bottom-up approach by means of a constraint-based parametric CAD modeller. In this way, a reciprocal frame can be explored and modified by the parametric arrangement of its generative elements, which, like a natural organism, grows in self-generating forms.

Persian architecture is characterised by shapes and patterns, which can be analysed through mathematical models. Beside 2D patterns, many of the traditional geometric ornaments are realised on 3D surfaces such as domes or vaults. Literature mainly addresses the 3D problem by means of a 2D scheme, which is an important and synthetic representation but is not exhaustive and lacks of clarity. This paper proposes a framework based on the integration of 2D drawings, as in the traditional approach, and a photogrammetric 3D model based on a sample of standard resolution images (tourist pictures). The framework is tested on a muqarnas, a characteristic Persian ornament, in order to study and analyse its modular design and hierarchy of elements. As a case study, the entrance iwan of the Shah Mosque in Isfahan, Iran, is considered. The result is a link between the 3D patterns and the geometry of architectural elements, which completes and overcomes their schematic 2D representation.