Section 9-4
1
Math 366 Lecture Notes
Section 9.4 – Geometry in Three Dimensions
Simple Closed Surfaces
A simple closed surface has exactly one interior, no holes, and is hollow.
A sphere is the set of all points at a given distance from a given point, the center. A sphere is a
simple closed surface.
A solid is a simple closed surface with all interior points. (see p. 615)
A polyhedron is a simple closed surface made up of polygonal regions, or faces.
The vertices of the polygonal regions are the vertices of the polyhedron, and the sides of each
polygonal region are the edges of the polyhedron. (see p. 615)
A prism is a polyhedron in which two congruent faces lie in parallel planes and the other faces
are bounded by parallelograms. The parallel faces of a prism are the bases of the prism. A
prism is usually names after its bases. The faces other than the bases are the lateral faces of a
prism.
A right prism is one in which the lateral faces are all bounded by rectangles.
An oblique prism is one in which some of the lateral faces are not bounded by rectangles.
To draw a prism:
1) Draw one of the bases.
2) Draw vertical segments of equal length from each vertex.
3) Connect the bottom endpoints to form the second base. Use dashed segments for edges
that cannot be seen.
A pyramid is a polyhedron determined by a polygon and a point not in the plane of the polygon.
The pyramid consists of the triangular regions determined by the point and each pair of
consecutive vertices of the polygon and the polygonal region determined by the polygon. The
polygonal region is the base of the pyramid, and the point is the apex. The faces other than the
base are lateral faces. Pyramids are classified according to their bases.
A right pyramid is one in which all the lateral faces are congruent isosceles triangles.
