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Geometrical relationships and interactions among hierarchical structures in homogeneous isotropic turbulence are investigated by identifying individual vortices of three different scales in the inertial subrange. Fourier bandpass filters are employed to extract the vortices, and each extracted vortex is replaced by a group of vortex segments with a cylindrical shape. The axes of neighboring vortices tend to be anti-parallel when the distance between them is equivalent to their diameter. Further, results indicate that a vortex is most strongly stretched by vortices twice the scale irrespective of the Reynolds number and the vortex scales. Then, the geometric relationships between the vortices being stretched and those that cause the stretching are analyzed, and the stretching is found to be particularly strong when the two vortices are orthogonal to each other.