A novel method and description of creating diversified complex original building forms roofed with a number of transformed folded shell units developed on the basis of a novel reference polyhedral network and arranged according to a reference surface with the negative Gaussian curvature is presented. For that purpose, specific reference polyhedral networks is are defined as a complex material deliberately composed of many regular tetrahedrons that are arranged regularly to obtain original attractive complex general building forms. The proposed method is a significant extension of the previous method for shaping roof structures with the positive Gaussian curvature and fills existing gaps in current scientific knowledge. The extended method enables the designer to significantly increase the variety of the created complex shell roof forms and plane-walled folded elevation forms of buildings and to define the shapes of their rod structural systems. It allows one to overcome the existing significant geometric and material limitations related to shape transformations of nominally flat rectangular folded steel sheets into different shell forms. The developed extension is based on formation of a set of properly connected tetrahedra as a material determining different (a) inclination of elevation walls to the vertical, and (b) distribution of many individual warped roof shells in accordance with the properties of a regular surface with negative Gaussian curvature. A number of the adopted specific sets of division coefficients (parameters) is used for determining the entire network and its complete tetrahedra. The presented description makes it possible to adopt appropriate assumptions and data and then employ the innovative method to obtain the expected characteristics of the unconventional building form shaped. The presented three different special forms created with the help of the novel method and the appropriately selected diversified values of the division coefficients of pairs of the vertices of a polyhedral reference network, a polygonal eaves network and points of a reference surface confirm the innovative scientific nature of the obtained results. The method has to be computationally aided due to the complexity of mathematical operations and the need to visualize the designed forms.
Keywords: complex substitute material; corrugated shell roofs; division coefficients; parametric polyhedral networks; polygonal networks; regular systems of shells; unconventional building free-forms.