The paper concerns geometrical shaping of shell structures composed of individual shells arranged effectively in space that is in a way similar to properties of a regular, geometrical surface with taking into account straight lines and planes normal to the base surface. The individual segments are made up of unidirectional folded flat sheets transformed into shell shapes. A freedom of transversal width increments of these sheets is assured while transforming, which ensures their possible small effort -such a deformation of a material intended for transferring functional loads but which makes restrictions concerning the shell sheets shapes. These shape restrictions are provoked by the strictly determined stiffness characteristics of the shell sheets and cause of the edge or discontinuous areas between adjacent shellssegments in the shell structure. The method of delimiting great diversity of effective, compound shell forms whose general shapes are close to regular, geometrical surfaces characterized by any sign of the Gaussian curvature is presented. Innovation of the way also consists in integration of the form of a whole building object (walls and shell roof). It is achieved by division of the elevation walls into flat areas contained in planes close to planes normal to the base surface as accurate as possible. The segment's directrices are also contained in these planes. The presented issues are the ground for elaborating a method of shaping of the light gauge steel shell structures and their further integration with whole building objects.

The article is an original insight into interdisciplinary challenges of shaping innovative unconventional complex free form buildings roofed with multi-segment shell structures arranged with using novel parametric regular networks. The roof structures are made up of nominally plane thin-walled folded steel sheets transformed elastically and rationally into spatial shapes. A method is presented for creating such symmetric structures based on the regular spatial polyhedral networks created as a result of a composition of many complete reference tetrahedrons by their common flat sides and straight side edges arranged regularly and symmetrically in the three-dimensional Euclidean space. The use of the regularity and symmetry in the process of shaping different forms of (a) single tetrahedral meshes and whole consistent polyhedral structures, (b) individual plane walls and complex elevations, (c) single transformed folds, entire corrugated shell roofs, and their structures allow a creative search for attractive rational parametric solutions using a few author’s parametric algorithms and their implementation as built-in commands of the AutoCAD visual editor or applications of the Rhino/Grasshopper program.

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The article concerns the unconventional architectural forms of buildings roofed with transformed shells made up of thin-walled steel fold sheets, and a parametric description of how they are shaped. Complicated deformations of flanges and webs, as well as the complex static–strength work of the folds in a shell roof, demand the creation of simplified models regarding the parameterization of such shells and their integration with the general forms of the buildings. To obtain favorable results, it was necessary to write computer applications because of both the complicated problems related to the significant limitations of the transformations, as well as the great possibilities of shaping shell roofs by means of directrices of almost free shape and mutual position. The developed procedures enable the prediction of shapes and states of all the folds in the designed shell. They take account of two basic conditions related to these restrictions, which guarantee that the folds encounter little resistance when matching their transformed forms to the roof directrices, and that their initial effort was as low as possible. The developed procedures required solving a number of issues in the fields of architecture, civil engineering, and structures, and are illustrated with an example of shaping one unconventional architectural form. The interdisciplinary study explains a new insight into shaping such forms.

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