Types of Pyramids

Date: 06/08/99 at 00:21:07
From: Rhiannon Lipman
Subject: Mathematical Pyramids

What are the types of pyramids? I know that a pyramid with a base that 
has four equal sides is a square pyramid, but what are the other types 
called and what do they look like?

Date: 06/08/99 at 01:29:58
From: Doctor Barrus
Subject: Re: Mathematical Pyramids

Hi, Rhiannon!

Good question! You're right - a pyramid with a base that is square is 
called a square pyramid. Most other pyramids are called by the name of 
their base. So, for example, a pyramid whose base has five equal sides 
(in other words, whose base is a regular pentagon) is called a 
pentagonal pyramid. A 6-sided (hexagon) base pyramid is called a 
hexagonal pyramid, a 7-sided (heptagon) one is called a heptagonal 
pyramid, etc.

There's one pretty important exception to that rule. It's the pyramid 
whose base is an equilateral triangle - a triangle with 3 equal 
sides. If the sides of the pyramid that go up from the base to the top 
of the pyramid are all this same length, too, then the pyramid is 
called a tetrahedron. This is an important pyramid. It has 6 edges, 
all of the same length, and 4 sides that are all exactly the same 
shape! It's been known for thousands of years. 

For a picture of a tetrahedron, see the Dr. Math FAQ:

http://mathforum.org/dr.math/faq/formulas/faq.polyhedron.html#tetrahedron   

or Peter T. Wang's Platonic Solids page:

http://www.ugcs.caltech.edu/~peterw/studies/platonic/tetrahedron.html   

I hope this is clear and has helped. Good luck!

- Doctor Barrus, The Math Forum
  http://mathforum.org/dr.math/