A cone has one circular base and a vertex that is not on the base.
as described on math.com
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A cone
The line or plane upon which a geometric figure is thought of as resting is called the base. A three-dimensional figure with a circular base and the top meeting at a vertex; it resembles a funnel cone.
a cone
A shape with a circular base and a vertex that isn't in the same plane as the base is called a cone.
A cone