Abstract: The model elementary flexor is a polyhedral panel represented by a four-angle star-like pyramid which is formed by thin elastic three-angle faces with hinge junctions. It has two symmetry planes which intersect the petals of flexor. An essential geometric property of the flexor is following: when the middle polyhedron is projected into the plane of the boundary, then each face is mapped to a triangle whose doubled intrinsic and extrinsic angles adjacent to the boundary are equal to ?/2?? Ta ?/2+? respectively, where ? is the third angle of the three-angle and it belongs to the interval (0,?/2). As consequence, the presented device is more general than its prototype, the right star-like pyramid “Model ideal flexor”, disclosed in UA Patent No. 54692. The invented device belongs to various areas of technique and industry where polyhedral shells with freely changed geometric forms are applied: architecture, aircraft construction, shipbuilding and precise instrument-making.