镶嵌几何在当代建筑表皮设计中的应用

Applications of tessellation in contemporary architectural surface design

以数学分析与案例分析相结合的方法,研究了建筑表皮设计中镶嵌几何的应用.论述了镶嵌几何学的基本原理,分析了平面周期性镶嵌和非周期性镶嵌的主要特点,以及在建筑表皮设计中的应用方式,并对典型的空间镶嵌单元,如长菱形十二面体、截顶正八面体等进行了探讨.结果表明,存在3种单一正多边形镶嵌模式和11种正多边形组合镶嵌模式,在建筑表皮设计中可以在其中加入随机性要素.非周期性镶嵌适合于表达当代的"复杂性"美学,空间镶嵌具有造型设计和结构设计方面的双重优势.从"以少博多"的基本原则出发创造性地运用镶嵌几何原理,可以提高建筑表皮设计的技术合理性与艺术表现力,拓展建筑设计思路,符合当代建筑设计向多学科融合发展的趋势.

Applications of tessellation in architectural surface design was discussed through mathematical analysis and case studies. The fundamental geometric principle was examined, then the characteristics and application methods in architectural surface design of periodic/aperiodic tessellation were analysed, and typical spatial tessellation units such as Rhombo-hexagonal dodecahedron and truncated octahedron were also explored. The results showed that three types of single regular polygon can be tessellated, and eleven types of compositional tessellations with regular polygons are possible. Random elements can be added into these patterns in architectural surface design. Aperiodic tessellation is suitable to express contemporary aesthetics of complexity, while spatial tessellation has advantages in both surface design and structural design. Based on the basic principle ＂doing the most with the least＂, creative applications of tessellation will enhance the technological rationality and the appearance of surface design, expand architectural creation manner, as well as positively responding to the tendency of architectural design to be interdisciplinary.