[2021] Creating novel nonperiodic patterns for flat and curved surfaces from a single pentagonal ele

Javan, A.R., Lee, T.U. and Xie, Y.M., 2021. Proceedings of the IASS Annual Symposium 2020/21. [Link]


Tessellations have been utilised for many novel architectural applications, as they can create striking surfaces by repeating a small number of different elements. However, most tessellations are limited to periodic arrangements and planar configurations.


This study systematically addresses these two limitations by developing a new type of nonperiodic pattern. We have developed a set of interesting nonperiodic patterns using triangle, quadrilateral, and pentagonal elements. A shape transformation method is proposed, which allows us to conveniently create a wide variety of innovative nonperiodic patterns. Using the transformation, we have designed a novel pentagonal element. This single element can be tessellated to form numerous nonperiodic patterns on a continuous surface with holes of up to nine different shapes, as shown in Figure 1b.


This paper shows various other nonperiodic patterns that can be formed using the proposed single solid element. We have built a physical prototype to demonstrate the beauty of such a pattern by using hollow 3D elements converted from 2D shapes considering waste minimisation. By extension, a repositioning method for pentagonal elements to rationalise a target 3D surface is proposed. It allows complex curved surfaces to be constructed from identical elements and therefore offers an opportunity to achieve economic constructions. Figure 1. Designing novel patterns from a single element: (a) a pentagonal unit element and (b) a nonperiodic pattern created from the element.