Geometric versatility of Abeille vault : a stereotomic topological interlocking assembly

Abstract

The Abeille flat vault, patented at the end of 17th century, consists of identical ashlars arranged in a woven-like pattern that generates their interlocking mutual support. In recent years, the availability of digital design and fabrication tools has caused new interest in the Abeille vault. Several studies investigate the interlocking principles through their application onto non-planar assemblies. This paper is a is a more systematic exploration into the underlying geometric interdependencies behind interlocking principles. It approaches the Abeille vault as a topological interlocking assembly (TIA), an assembly where basic identical elements of a special shape are arranged in such a way that the whole structure can be held together by boundary constraint, while locally the elements are kept in place by kinematic constrains imposed through the shape and mutual arrangement of the elements. The paper looks at the full potential of the Abeille vault application and studies the relation between the surface geometry and TIA