Tessellation art3/22/2023 ![]() Within this geometrically defined and ordered universe, nothing stands in isolation or ambiguity everything is interrelated and carefully positioned in an intricate hierarchy. Religious beliefs about the cosmos, geography, the human body, and constructed forms are all underpinned by a consistent spatial sensibility anchored in medieval geocentrism. Referencing a wide range of mystical texts, and with a special focus on the works of the great Sufi master Ibn >Arabiμ, Akkach introduces a notion of spatial sensibility that is shaped by religious conceptions of time and space. The book features many new translations, a number from unpublished sources, and several illustrations. Samer Akkach demonstrates how space ordering in premodern Islamic architecture reflects the transcendental and the sublime. This fascinating interdisciplinary study reveals connections between architecture, cosmology, and mysticism. Therefore, research on the application of tessellation in architectural geometry design is of great necessity in architecture studies. The development of Computer technology enables tessellation to be more powerful, as seen in surface control, surface display and structure design, etc. In history, tessellation was applied into skins or decorations in architecture. Both Geometry and Crystallography, the latter of which is the basic theory of three-dimensional tessellations, need to be studied. Besides, some special types of tessellations such as Voronoi Tessellation and Delaunay Triangles are also included. In terms of dimensions, there are two- dimensional tessellations and three-dimensional tessellations in terms of symmetry, there are periodic tessellations and aperiodic tessellations. Tessellation has been found since the birth of civilization. ![]() Tessellation plays a significant role in architectural geometry design, which is widely used both through history of architecture and in modern architectural design with the help of computer technology. 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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