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We explore new opportunities for solar physics that could be realized by future missions providing sustained observations from vantage points away from the Sun-Earth line. These include observations from the far side of the Sun, at high latitudes including over the solar poles, or from near-quadrature angles relative to the Earth (e.g., the Sun-Earth L4 and L5 Lagrangian points). Such observations fill known holes in our scientific understanding of the three-dimensional, time-evolving Sun and heliosphere, and have the potential to open new frontiers through discoveries enabled by novel viewpoints.