![]() ![]() The study of the mural symbols in ancient Egypt, the murals in the Alhambra, the manuscripts of Escher and the window lattice in ancient Chinese architecture profoundly reflects the basic operation principle of crystal group in shaping the skin form of architecture. Crystallographic group with regular symmetry and the operation principles reflected by it is one of the most important rules and methods of form and pattern processing in skin design. The complex and diverse forms of today's building skin hide profound mathematical logic relations and operation rules of form generation. Under the dual constraints of industrialization and digitalization, the building skin and structure are further integrated to form standardized units to meet the requirements of architectural performance, industrial prefabrication and “complexity” aesthetic characteristics. Our findings demonstrate the highly auxetic property of rotating polyhedral systems, which allow the design of novel architected materials useful, for example, in biomechanical applications. Experimental results exhibited an excellent agreement with computational predictions in terms of elastic modulus and auxeticity, showing a value of Poisson’s ratio up to -1.3 for one of the designs. The specimens were tested under uniaxial compression and simulated through finite element analyses. Focusing on the most promising auxetic mechanisms we designed chiral architectures that replace the ideal hinges at the corners with curved-shape ligaments, and validated these configurations through 3D printed specimens. The kinematic results highlight the peculiar NPR of the system, whose values are nearly constant over significant strain ranges. Through a kinematic model of the proposed rotating structure, we evaluate the auxeticity of the system by varying the geometrical parameters of the polyhedrons composing the elementary cell of the structure. The work presents a novel polyhedral mechanical metamaterial based on rotating triangular prisms connected by their corners, which possesses the ability to attain large values of negative Poisson’s ratio (NPR). As well as providing a deeper understanding of such tessellation methods, this study will serve as a basis of reference for future studies in this field. In this paper, the geometric design principles, combination methods and iteration processes of the examples are also presented. For this reason, within the scope of this paper, the applied examples of the tessellations in buildings from past to present are examined which include both static and kinetic ones. Due to their great potentials, more studies should be conducted on the tessellations. Because the tessellation plays a significant role in architecture in terms of geometrical or structural design, the interest on this topic has been increased in recent years. Two- and three-dimensional examples of the tessellations can be seen in contemporary architecture either as façade elements or patterns used for structural elements. The tessellation can be reviewed under three categories such as regular, semi-regular and demi-regular tessellations. ![]() The tessellation has still been used in contemporary architecture since it not only allows creating the geometrical surface in an order but also provides multi-functionality to the surface when applied as shading elements. Through the history, different patterns have been used by many cultures for various applications ranging from decorative covering elements to multi-functional latticework screens. Based on Roman mosaics, the tessellation has an important place in architecture since the ancient times. Tessellation, which has examples of use in art and architecture, is the covering of a surface using one or more geometric shapes without overlapping or gaps.
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