Net of a Hexagonal Pyramid

Date: 02/05/2001 at 20:02:26
From: Sonia
Subject: Net

How would you draw a hexagonal pyramid and a rectangular prism in net 
form?

Date: 02/06/2001 at 11:56:02
From: Doctor Peterson
Subject: Re: Net

Hi, Sonia.

I believe the kind of "net" you are asking about is a flat drawing 
that can be folded up into the shape you want. In both cases, you can 
start with the base (a hexagon or a rectangle), then add the sides, 
folded down flat; and finally, for the prism, attach the top to one of 
the sides. Here are my attempts at both, to suggest how it should 
look.

Hexagonal pyramid: fold all six points up so they meet:

                        |
                        |
                       | |
                       | |
                      |   |
      ----            |   |            ----
        ----------   |     |   ----------
          ---     ---+-----+---     ---
             --     /       \     --
               --  /         \  --
                 -*    base   *-
               --  \         /  --
            ---     \       /     ---
          --      ---+-----+---      --
        ----------   |     |   ----------
      ----            |   |            ----
                      |   |
                       | |
                       | |
                        |
                        |

(All 12 edges of the side faces must be the same length, for a 
regular pyramid.)

Rectangular prism: fold the four sides up, then fold the top over:

                +-------+
                |       |
                |  back |
                |       |
                |       |
      +---------+-------+---------+-------+
      |         |       |         |       |
      |         |       |         |       |
      |  left   |bottom |  right  |  top  |
      |         |       |         |       |
      |         |       |         |       |
      |         |       |         |       |
      +---------+-------+---------+-------+
                |       |
                |       |
                | front |
                |       |
                +-------+

Pay attention to which edges have to have the same length, so that 
when they are folded they will meet properly. For example, there are 
eight edges whose length is the height of the box.

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