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Rhombicuboctahedron


Date: 05/14/99 at 13:37:13
From: Jenna
Subject: Rhombicuboctahedron

We have to make a soccer ball out of different shapes. We chose the 
rhombicuboctahedron. It asks us for the net. We don't understand how 
to get the net. Please explain and send us a picture. Thank you


Date: 05/14/99 at 17:11:00
From: Doctor Rick
Subject: Re: Rhombicuboctahedron

Hi, Jenna.

To me, "soccer ball" means one particular polyhedron, the truncated
icosahedron, which is the basis for the stitching pattern on a real 
soccerball. You can make sort of a ball out of a rhombicuboctahedron, 
but it won't be as "round."

Here are patterns for making paper models of a rhombicuboctahedron 
and other polyhedra, by G. Korthals Altes:

http://www.geocities.com/SoHo/Exhibit/5901/indexe.html#papermodels   

Once you've made the model, it is easier to figure out the net. 

One way to think of the net of a polyhedron is to imagine poking a 
hole in one face of the polyhedron and then stretching it out as if it 
were made of rubber, until the whole thing is flat. The edges of the 
face in which you poked the hole will form the outside of the net.

The net is a pattern of lines, one for each edge of the polyhedron, 
joined in the same manner as the edges of the polyhedron; but you 
don't need to worry about keeping them the same length, or even 
keeping them straight. Just don't let them cross. Here is an example, 
the net of a cube:

  +-------------------+
  |\                 /|
  | \               / |
  |  \_____________/  |
  |   |           |   |
  |   |           |   |
  |   |           |   |
  |   |           |   |
  |   |           |   |
  |   |___________|   |
  |  /             \  |
  | /               \ |
  |/                 \|
  +-------------------+

It's up to you to draw the net of the rhombicuboctahedron.

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Geometry
High School Polyhedra

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