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Purpose. Defining features of the building construction vest, as part of the National Iranian costume improvement in the method of constructing the armhole, to create a mathematical model of the surface and the construction of scans. Methodology. We used modern methods of investigation of initial data geometric curve-fitting surfaces of order 2, with the condition to minimize the initial data. Findings. The studies identified design features contemporary women armholes of his waistcoat, taking into account the structural arrangement of the national costume northwestern regions of Iran. The optimal methods of construction design armholes products using modern computer technology, which enables accounting model design changes at the design stage. Originality. In this paper, we propose a new method for constructing a spatial line armholes, based on its profile projection as a line of mutual intersection of profile-projecting cylinder, which is a guide profile projection armholes with a cylindrical surface in general position. [ABSTRACT FROM AUTHOR]