The Structural Transformation of Concave Cupolae of Fourth Sort Using Different Variants of Constructive Procedure, 4th International Scientific Conference on Geometry and Graphics

Abstract

Concave Cupolae of fourth sort (CC IV) are polyhedra which lateral surface is created by folding a quadruple strip of equilateral triangles, while the bases are regular polygons. The unit cell that forms the deltahedral lateral surface by radial sequenceing around the axis of the solid is composed of two spatial hexahedrals. These unit cells are linked together in its upper zone by spatial quadrihedals, which consist of four equilateral triangles grouped around a common vertex. Over the same polygonal base, there can be formed four diverse Concave Cupolae of IV sort, using different variants of constructive procedure. In this paper, the application of the program for modeling the lateral surface of concave cupolae of IV sort, using the software package MATLAB, allows visual monitoring of the structural transformation of the concave cupolae of IV sort, for different polygonal bases and different variants of constructive procedure.