Stellations of the Dodecahedron

arrowStellations of the Dodecahedron Applet (below) doesn't work even though you installed Java?
 Run the Stellations of the Dodecahedron Web-Start Application instead.
 This downloads a jnlp (Java Web Start) file that tells Java how to run the Stellations of the Dodecahedron outside of your browser.
 See my Java Web Start notes.
Keyboard Commands:
 s Stereo mode
 r Rotation (on/off)
 h Hollow (on/off)
 b Big (on/off)
 d Detach/Attach
 e Edges (on/off)
 l Lighting (on/off)
 m Morphing (on/off)
 f Fast (on/off)
Object Selection:
 1 Regular Dodecahedron
 2 Small Stellated Dodec
 3 Great Dodec
 4 Great Stellated Dodec
 c Cycle objects
screen shot

Click the image to enable keyboard commands.
If you don't have 3D glasses, type "s" to switch the stereo mode for "look crossed" viewing.
Manually rotate by dragging with the mouse.
If you press the same numeric key (1 through 4) twice, the morphing will freeze.
For Browser Requirements, see below.

More Java applets here.

About Keyboard Commands:

About the 3D Objects


The "core" object is the regular dodecahedron. It is enclosed by 12 pentagonal "faces". Each face lies in a different infinite plane. Thus the dodecahedron defines 12 infinite planes. The edges and vertices of the dodecahedron occur on intersections of these planes.

The stellation process works because the 12 planes have additional intersections outside of the core dodecahedron (it wouldn't work for a cube). We stellate a polyhedron by extending all its faces until they intersect again along new edges.

The java applet on this page illustrates this process. As the applet morphs, you can watch the faces expand to create new intersections. (This is easier to see if you turn off "Big" mode by pressing the "b" key, and stop the rotation by pressing the "r" key.)

Related Links

Implementation Notes

I made this applet as a test for a pure-Java 3D rendering package that I wrote.
I opted for the "press a key" user interface for a couple of reasons:
1. Laziness (this was just supposed be a quick demo of my renderer)
2. It fits -- it's a lot easier than trying to click a button or drop a choice-box while you are looking cross-eyed at a 3D image.


The information about star polyhedra comes from H.S.M. Coxeter's book "Regular Polytopes" (Coxeter01).

Browser Requirements

This is a Java 1.1 applet. See my Java page for Browser Requirements.

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