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Basic
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Octahedrons

Basic Octahedron

Start with a Stellated Octahedron
1. Begin with a cube
2. Use the line tool to connect corner to corner:
3. Connect all corners:
4. Delete all the edges of the original cube:
Color the faces (you should have 8 colors)
Select the entire model, press space bar and click on an edge. Select Intersect Faces>with Selection:
Delete the 8 pyramids:

Stellated Octahedron

Begin with a cube
Use the line tool to connect corner to corner:
Connect all corners:
Delete all the edges of the original cube:

Truncated Octahedron

Begin with an octahedron
Press the spacebar and CTRL click on a line. Select Divide
Divide each line segment into thirds, then use the Line tool to connect all the endpoints
Divide all the segments and connect all the endpoints the
Delete the pyramids
This is known as a truncated octahedron:

Sources:http://www.3dvinci.net/mathforum/ConicSections_StudentVersion.pdf
http://sketchup.google.com/
http://mathworld.wolfram.com/GoldenRatio.html
http://www.vashti.net/mceinc/golden.htm
http://library.thinkquest.org/25672/fibonacc.htm

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