A linear construction truss comprising a hollow shell with a square cross section and a core composed of linked tetrahedra, and a method of manufacturing of said linear construction truss comprising the steps of bending sheet metal strips to create a tetrahedral core such that the faces of the tetrahedral alternate between approximately 109.5 degrees and approximately 289.5 degrees throughout the length of the sheet metal strips. Strips of sheet metal are further bent to form a hollow shell with a square cross section rigidly attached to the core in a spiral pattern. The triangular faces are chamfered to better enable the connection between the core and hollow shell. The sheet metal is cut in such a way such that the perforations do not impinge on the edges of the tetrahedral.