Possibilities of Deltahedral Concave Cupola Form Application in Architecture

Abstract

In recent years, we are witnessing an increasing use of triangular modular building systems, which, especially in representative objects, almost push out the orthogonal system. Considering that deltahedra are assembled of equilateral triangles matching system, we investigated a possible application of such polyhedral forms in geometry of architectural edifices. Deltahedral concave cupola with a regular polygonal base is formed by connecting two concentric regular polygons: n-gon and 2n-gon by multiple series of equilateral triangles. Lateral surface of the cupola is obtained by folding a net of equilateral triangles to a concave polyhedral surface. The paper analyzes the prospect of such surfaces in architecture, not only in the geometry of roof structures, which is imposing as an obvious solution, but also as a structural skeleton of the whole building. The analysis includes several criteria for evaluating the suitability of these forms for practical application: their static properties, atmospheric effects, functional analysis, preferential use of certain constructive systems, and finally, aesthetic properties of these forms.