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An osculating torus is one in which the major and minor radii are the same. To construct one, think of drawing a circle, then drawing a line that touches the circle tangentially, and then rotating the circle all the way round this axis. It is referred to as osculating, or "touching closely," because the point of contact between the circle and line remains stationary as you rotate, and is the spot at the middle of the torus where the torus "touches itself in all directions." The osculating torus is the limiting case between the ordinary torus (donut shaped) where the major radius is bigger than the minor one, and the apple torus where the minor radius is a bit bigger than the major radius.
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