The Torus: Perpendicular Sweep

The torus is the fourth solid — swept perpendicular to the around-axis, not tangent like the cylinder/sphere/cone. Being offset from the central axis makes the torus sweep perpendicular instead of tangent. Three torus types by radius ratio R vs r: Loop torus (R>r, central hole visible, the standard donut), Horn torus (R=r, hole shrinks to a single point, self-tangent), Spindle torus (R<r, self-intersecting, two pinch points at poles). Volume = 2π²Rr² = (πr²)(2πR) by Pappus theorem. Magnetic force is torus topology — closed loops, no monopoles — this is why there are no magnetic monopoles. Perpendicular sweep maps to the right-hand rule.

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