The optimization process leading to the tessellation of the first geodesic dome structure, the first Planetarium of Jena

Abstract

The tessellation of the first built geodesic dome structure (the first planetarium of Jena, designed by Walther Bauersfeld, built 1922–23) has been unknown until recently. While original documentation of the tessellation has been published, the concept behind it has not been uncovered. This article presents the evolution of the final tessellation based on Bauersfeld’s hand-written notes found in the Zeiss Archives in Jena. Bauersfeld contemplated various methods of subdivision and performed detailed calculations and optimality analysis on them—preceding the theoretical studies on the tessellation of geodesic domes by almost 30 years. His key findings, relevant and comparable with later studies are highlighted. The concept of the presumably final tessellation is revealed to be the equal-area triangulation of the sphere—which has to the author’s knowledge not been considered ever since for geodesic domes. The remarkably simple algorithm applied did not result in a theoretically exact solution (well known to Bauersfeld), but as shown in this article in engineering terms it got sufficiently close. Moreover, it is concluded that the resulting tessellation excels in terms of important parameters (e.g. edge length ratio, number of different edges) compared to existing practical and theoretical solutions.