Einar Thorsteinn and FANG geometry: An Unveiling of Symmetry

FANG - Fivefold Symmetry - All Space Filling - Non-Periodic - Geometry

FANG visualisation

Einar Thorsteinn (1942 – 2015) devoted much of his life’s work to a remarkable concept, FANG. This acronym stands for Fivefold Symmetry – All Space Filling – Non-Periodic – Geometry, and it became a testament to Thorsteinn’s enduring fascination with geometric design and symmetrical forms.

The Integral Role of the T-Quanta Module

In his journey, one element that especially intrigued Thorsteinn was Buckminster Fuller’s T-Quanta Module. This singular tetrahedron played a pivotal role in his exploration of FANG. By employing mirror and scaling transformations, Thorsteinn was able to manipulate this module, which subsequently led to the creation of fivefold symmetric units in space.

FANG report title page Polyhedral System for Finetuning Fivefold Symmetry Space with Reference to Quasicrystal Growth

FANG report (2004) by Einar Thorsteinn – Cover Page

Insights Shared in “FANG Report I”

Thorsteinn decided to share his enlightening observations with the world through his 2004 essay, “FANG Report I”. In this piece, he delved deep into the intricate interplay and correlation between vertices, angles, surfaces, and volumes within the FANG framework. His systematic approach threw light on the numerous details hidden within the complex structure of FANG.

Fang report page 33 Einar Thorsteinn

FANG report (2004) by Einar Thorsteinn – Page 33 excerpt

Amman Bars: The Two-Dimensional Reflection of FANG

Interestingly, FANG doesn’t exist solely in a three-dimensional world. It also has a reflection in the two-dimensional realm, known as the Amman bars. Much like FANG, the Amman bars serve as a demonstration of the enormous potential inherent in geometric design when symmetry and proportion are brought into play.

Fang report page 10 Einar Thorsteinn

FANG report (2004) by Einar Thorsteinn – Page 10 excerpt

The Enduring Legacy and Impact of FANG

Throughout his exploration of FANG and other geometric forms, Thorsteinn never failed to showcase his profound understanding of space, symmetry, and geometry. Today, his body of work stands as a symbol of precision and aesthetic appeal, continually inspiring enthusiasts and practitioners in the realm of geometric design. Furthermore, the general idea of FANG avenues for potential advancements in numerous fields, from architecture and design to physics and engineering.

Einar Thorsteinnn at Studio Olafur Eliasson

Einar Thorsteinn at Studio Olafur Eliasson in 2011 (Image: Studio Olafur Eliasson)


Personal Encounters with Einar Thorsteinn

I had the unique opportunity to meet Einar at Studio Olafur Eliasson in 2010. He was a captivating personality and a constant source of inspiration. Many of my later explorations find their roots in his pioneering research. Although we had different approaches to using software tools, we both held a shared admiration for physical models. I recall one occasion when I was grappling with a complex geometry description in a script. When I sought his guidance, instead of a direct answer, he left me with a profound statement that has stayed with me ever since:


“You know, sometimes the computer just does what it wants.”


And with that, he simply looked at me.”



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