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Pyramids

Another interesting kind of polyhedron is a pyramid. A pyramid is the
union of a polygon with all of the
segments that have one endpoint on the
polygon and the other endpoint at a specified
point in
space that is *not in the same
plane as the polygon.* The
polygon is the *base* of the pyramid, and the fixed
noncoplanar point is the
*vertex* of the
pyramid. The faces of the pyramid that share the vertex are the lateral
faces of the pyramid, and their intersections with each other are called the
lateral edges.

Figure %: A pyramid

Every lateral face of a pyramid is a triangle. The
segment perpendicular to the plane of
the polygon with one endpoint at the vertex and one in the plane is called the

*altitude* of the pyramid.

A regular pyramid is a special kind of pyramid (ironic, huh?) whose base is
a regular polygon and whose altitude intersects the
plane of the base at the center of the base. This means that all of the lateral
edges and lateral faces are congruent.

Figure %: A regular pyramid

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Cones

A more general form of a pyramid is a cone. A cone is composed of a
simple closed curve in a plane and all of the line
segments that join that curve with a fixed point
not in the plane of the curve. The simple closed curve is called
the *base* of
the cone, and the fixed noncoplanar point is the vertex. The segments that
connect the base with the vertex form the *lateral surface* of
the cone. The
segment perpendicular to the plane of the base with an endpoint at the vertex
and an endpoint on the plane is the *altitude of the cone.*

Figure %: A cone

A circular cone is a special kind of cone whose base is a
circle. A right circular cone is a
circular cone whose altitude intersects the plane of the circle at the circle's
center.

Figure %: A right circular cone

It is easy to see the close relationship between pyramids and cones. The only
difference is the base--a pyramid is a cone with a polygonal base.