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In mathematics, a cone is the quadric surface generated when a line is rotated around a fixed point (called the apex), at a fixed angle from another line (called the axis), both lines passing through that fixed point. It also can be described as 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.

A cone is represented in Cartesian coordinates by the equation

ax² + by² + cz² = 0.

The shape called "cone" in more colloquial usage is half of a mathematical cone, being divided at the apex; or less than half if it is cut off at some distance from the apex. Common cone-shaped objects are an icecream cone (with the point down); plastic traffic cones on roads for temporarily guiding traffic (with the point up); and pine cones (spindle-shaped seed pods).

A cone with its apex cut off by a plane parallel to its base is called a conical frustum.

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