Prism—A prism is a polyhedron with
two parallel, congruent faces that make
up the bases of the shape; the other, later-
al faces are considered to be parallelo-
grams. If the lateral faces are rectangles,
the prism is called a right prism.
Parallelepiped—This strange-sound-
ing polyhedron is one that has all its faces
as parallelograms, or a prism with paral-
lelogram bases. The most familiar paral-
lelepiped is a simple box—also called a
rectangular parallelepiped—that has rec-
tangles for all the six faces. (For more
about these figures, including how to cal-
culate their areas, see elsewhere in this
chapter.)
How are spheres described?
A sphere in solid geometry is considered
to be the set of points (or the “skin” of
the sphere) in three-dimensional Euclidean space that are equidistant from the
sphere’s singular, central point. Or, more simply, a sphere is a perfectly round, three-
dimensional object. The term “sphere” also extends into other dimensions; for exam-
ple, a sphere in two dimensions is also called a circle.
What is spherical geometry?
Spherical geometry is the study of objects on the surface of a sphere; this differs from
the type of geometry studied in plane or solid geometry. In spherical geometry, there
are no parallel lines, and straight lines are actually great circles, so any two lines meet
in two points. In addition, the angle between two lines is the angle between the planes
of the corresponding great circles. There are also entities called spherical triangles(or
Euler triangles), when three planes pass through the surface of a sphere and through
the sphere’s center of volume; they have three surface angles and three central angles.
There are also spherical polygons,in which a closed geometric object on the surface
of a sphere is formed by arcs of great circles.
187
GEOMETRY AND TRIGONOMETRY
The Greek philosopher Plato first described the five
regular solids known as Platonic solids in his book
Timaeus. Library of Congress.