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In mathematical terms, a cone is the surface generated when a line is rotated around a fixed point, at a fixed angle from another line (called the axis), both lines passing through that fixed point. It also can be said that it is the locus of all the points belonging to all the lines that pass through a given point, and that intersect at that point at a fixed angle to the axis line.

The shape called "cone" in more colloquial usage is half of a mathematical cone, being divided at the fixed point.