Creating a Nine-Sided Polyhedron

Date: 12/9/95 at 16:54:47
From: Anonymous
Subject: Nine sided polyhedra

We at the Gordon School, East Providence, have been studying polyhedra 
for many years.  The students always want to know about the odd shaped 
polyhedra.  We found the heptahedra picture, but we can't find out if a 
nine-faced polyhedron can be made.  Do you know where we could find a 
picture of it if it can be made?  Thanks. 

Maggie Holmes for the teachers of Gordon School

Date: 2/28/96 at 15:58:40
From: Doctor Ken
Subject: Re: Nine sided polyhedra

Hello!

The answer is yes, a nine-faced polyhedron can be made.  In fact, you 
could probably construct some actual models of them yourself.  Here are 
a couple of different ways you could do it:

1) This was suggested by Doctor Jodi, another Math Doctor here.  If you 
have a 7-sided polygon (poly GON, not polyhedron), then you can just 
make a prism that has that polygon as its bases.

2) Imagine a block of cheese that's in the shape of a cube.  It has six 
sides.  Now take a knife and lop off one of the 8 corners.  You've now 
created one more face than you had before, right?  So you just 
constructed a 7-hedron.  Similarly, you could keep going and chop off 2 
more corners to get a 9-hedron.  

Both of these methods will generalize to show that you can make any 
n-hedron where n is greater than 3.

- Doctor Ken,  The Math Forum