Tessellation Patterns as Structural Elements


Photo by: Andy Holmes on Unsplash

Architectural design is constantly evolving, challenging our design abilities as we move through the 21st century. Designing spaces for people, creating concepts, and taking care of clients are what usually drive design work. However, what would happen if we allowed the structure of a building to drive these elements? Focusing on the bones of buildings as a creative piece not only would impact the user experience but the form and function of the building itself. Architects and designers can begin to explore this ideology through the use of tessellation patterns as structural elements.
A tessellation is defined as a shape that is repeated, covering a plane without any gaps or overlap. They all have a specific algorithm/pattern that defines the organic or rigid formation. While tessellations are commonly created as 2D elements (some as 3D), they work seamlessly as structural supports in architecture. There are 5 main tessellations that serve as structural elements today: the Diagrid, Delaunay Triangulation, Voronoi Pattern, Delaunay and Voronoi Combination, and the Phelan-Weare Systems.
  • Diagrid: Diagrid structures are becoming more and more common in today’s world. They are created using a diagonal framework that supports the structural load of the building. Diagrids are created based on the height of the building in relationship to the Optimal Angle of the diagonal members. By arranging the structural supports on the exterior, creating an exoskeleton leaves a column-free interior, which invites a stronger designed building.

Photo By: https://www.semanticscholar.org/paper/Investigation-of-Shear-Lag-Effect-in-High-rise-with/1ddc138fab628f99131beba73a085d4bc7ca2ef4

  • Delaunay Triangulations: The Delaunay Triangulation is a particular way of joining points in order to create a mesh. The tessellation is constructed using circumcircles, which are created by joining the triangle’s 3 vertices together using a circle. There are never any overlaps between circles, and the triangles are created based on the point’s maximum angle. The Delaunay Triangulation is commonly used today as facades and/or skins, and we briefly notice it as a space frame/structural application.

Photo By: https://en.wikipedia.org/wiki/Delaunay_triangulation

  • Voronoi Patterns: Like the Delaunay Triangulation, the Voronoi Pattern is a pattern created by the division into regions based on a set of given points. Each region is called “seeds” or “sites” when the points are joined together but are also called “Voronoi Cells!” Commonly seen in architecture and design today, we notice the Voronoi Pattern in a structural sense as a façade or a shell. The tessellation could also be used as a space frame, but there would need to be further exploration on that.

Photo By: https://w7.pngwing.com/pngs/678/642/png-transparent-voronoi-diagram-attractor-mathematical-diagram-point-others-miscellaneous-angle-rectangle.png


  • Delaunay + Voronoi Combination: The Delaunay Triangulation and the Voronoi Pattern are very complimentary! When overlayed on one another, they create a new tessellation. The center points of the Voronoi Cells align with the vertices of the Delaunay Triangulation, and the center points of the Delaunay triangles align with the vertices of the Voronoi Diagram. Structurally, this theorem is best used as a space frame, but this theorem has not been explored due to the two patterns being used separately.

Photo By: https://www.researchgate.net/figure/Delaunay-triangulation-solid-lines-and-Voronoi-diagram-dashed-lines-for-20-points_fig1_324045163

  • Phelan-Weare Systems: Finally, our last tessellation is the most complex, the Phelan-Weare System. Consisting of hexagons and pentagons, this tessellation is best perceived in 3D! Each shape that makes up the Phelan-Weare system has equal volumes. Today, it is structurally shown as a space frame, with only a few built structures! It is a VERY uncommon method.

Photo By: https://www.researchgate.net/figure/The-Weaire-Phelan-structure_fig6_228971765

The creation of these tessellations is not as difficult as it may seem! The architectural design software, Grasshopper, a plug-in tool for the Rhinoceros software, would best be used. Grasshopper uses algorithmic and programming methods to create different structures, patterns, or geometries. Thankfully, creating tessellations in Grasshopper is easier than it seems. The Voronoi pattern is already a component that resides in the interface! You simply add it as a component to your project, and the tessellation is formed. The same process goes for the Delaunay Triangulation as well. The Delaunay Triangulation is also a component in Grasshopper, making these tessellations easily accessible. Any other tessellations you want to create will have to be designed using their specific algorithm, meaning you will have to find the right components and definitions for them to be created. Another tool to use when it comes to tessellations is Lunchbox, which is a plug-in for Grasshopper. It is used mostly to create more mathematical shapes versus organic forms but makes the organic forms buildable. It highlights a mixture of paneling creation, structural creation, and algorithmic creations. LunchBox is also helpful in terms of node design, which is crucial towards the structural loads for the tessellations.


One example of tessellations as structural elements in architecture today is the famous Water Cube. The Water Cube designed by PTW Architects is in Beijing, China. Completed in 2008 for the 2008 Beijing Olympics, this 32,000 sq. meter building reflects the use of the Phelan-Weare tessellation. PTW found inspiration for the structure based on the geometry of soap bubbles and cladding with ETFE pillows that looked like bubbles. There are 22,000 structural elements in the design and about 4,000 cladding panels. The Phelan-Weare system in the Water Cube is used as a space frame, and all the members are framed into the nodes. In doing so, this technique is a perfect energy-absorbing structure for Beijing, which experiences many earthquakes. The roof is made from 7 different-sized bubbles, and the walls are made from 15 different-sized bubbles. The Phelan-Weare structure is shown on the interior as well, giving each space an organic, interesting experience.

Photo By: https://www.arup.com/projects/chinese-national-aquatics-center

As complex as these tessellations may seem, they are not difficult to create. Design Collaborative can further explore these elements with the use of Grasshopper and Lunchbox technology, designing structure, interior spaces, and facades. Designing the bones of buildings is just as important as the conceptual design of the building, and tessellations can be the first step into this process. Each tessellation proposes a truly remarkable, extremely purposeful, and well-crafted design, that ultimately improves people’s worlds


Written By:
Abigail Bulmahn
Architectural Intern
Design Collaborative