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What Constitutes a Prism?


Date: 06/10/99 at 17:48:54
From: Kelsey Sullivan
Subject: Geometry, 3-D objects

If I am looking at a 3-dimensional object that's shaped like a 
triangle, how do I know if it's a prism? I have the same question 
about rectangles.

Sincerely,
Kelsey


Date: 06/11/99 at 12:16:44
From: Doctor Peterson
Subject: Re: Geometry, 3-D objects

Hi, Kelsey.

You can think of a prism this way: Take any polygon, such as a 
triangle or rectangle, and imagine holding it flat while moving it 
straight in some direction. Now imagine that wherever it goes it 
leaves a trail in the air. The shape you get will be a prism:

Move this shape in the direction shown

                        \
                         \
                      +---\----------------------+
                    /......\.................../
                  /.........\................/
                /............\............./
              /........................../
            /........................../
          +--------------------------+

and it makes this prism:

             +--------------------------+
           /........................../  \
         /........................../     \
       /........................../        \
     /........................../           \
   /........................../              \
 +--------------------------+                 \
  \                 \        \                 \
   \                 +--------\-----------------+
    \              /...........\............. /
     \           /..............\.........../
      \        /.................\......../
       \     /....................\...../
        \  /.......................\../
         +--------------------------+

So if two opposite faces are parallel and congruent (the same shape 
and size), and the edges connecting corresponding vertices (corners) 
of these faces are all parallel, then it is a prism. The 
parallelepiped above is a kind of prism; if you replace the shaded 
parallelograms with any polygon, it will still be a prism. Here's a 
triangular prism:

      +-----------------------------------+
      |  \............................./  |
      |     \......................./     |
      |        \................./        |
      |           \.........../           |
      |              \...../              |
      |                 +                 |
      |                 |                 |
      |                 |                 |
      |                 |                 |
      |                 |                 |
      |                 |                 |
      |                 |                 |
      |                 |                 |
      |                 |                 |
      |                 |                 |
      +-----------------|-----------------+
         \..............|............../
            \...........|.........../
               \........|......../
                  \.....|...../
                     \..|../
                        +

You can see some pictures of different prisms on our FAQ page:

 http://mathforum.org/dr.math/faq/formulas/faq.prism.html   

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Definitions
High School Geometry
High School Higher-Dimensional Geometry

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