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### Creating a Nine-Sided Polyhedron

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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
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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

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Associated Topics:
Middle School Geometry
Middle School Polyhedra

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