So far we've only been studying geometric figures that exist in a
plane. Now that we understand the basics of
plane geometry, we can take a brief look into the world of
three-dimensional figures and shapes. Such three-dimensional objects have
length, width, and a new third dimension, depth; they
are known as geometric solids. To understand a geometric solid, we study
the surface that forms its boundary. Such a surface does not have volume,
but the region it encloses, the geometric solid, does.

The variety of geometric solids in existence is limitless, so we have to
restrict the kinds that we study. We will concern ourselves with geometric
solids that are bound by polyhedrons and other simple surfaces. Polyhedrons
are special kinds of surfaces that are bound by parts of intersecting planes:
polygons.

As we study surfaces, you'll probably notice many similarities between surfaces
and figures in plane geometry. Throughout geometry, a given geometric figure in
a certain dimension often has a counterpart in other dimensions. A
segment's relationship to a
line is much like that between a
polygon and a
plane, and a polyhedron and
space. The main difference between these
pairs of geometric figures is which dimension they reach. If a concept is
difficult to understand in a certain dimension, it might be helpful to think
about that concept's counterpart in another dimension--probably a lower one--to
try to understand it better. The greater the dimension, the harder things
become to visualize, so simplification may come from reviewing lesser
dimensions.

After polyhedrons are discussed in general, we'll introduce specific types of them,
including prisms, pyramids, and regular polyhedrons. As we study
these, we'll also see their counterparts in ciruclar
form--surfaces with a similar shape that are partially bound by circles instead
of polygons. Such surfaces include circular cylinders, cones, and
spheres.

Like the previous topic of circles, in the following lessons geometric surfaces
will be introduced and defined, but not explored in full. That will have to
wait until the SparkNotes in Part 2 of Geometry, when the surfaces
are united
with their interiors to form geometric solids. Then we can look more closely at
the applications of the properties and definitions we learn here. For now,
we'll study the surfaces that form the boundaries of geometric solids, and their
properties. It all starts when a third dimension is introduced, and different
planes intersect.