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PaperCut home page on SourceForge.net
Stellated icosahedron

Samples will be moving to the Gallery... check back soon

4 Feb 2006 - Finally released a new version, 1.0.286, which supports Kepler's Stella Octangula (pictured here) and k-stellation. K-stellation is just a word I invented for stellation where you break down each triangular face into four parts (like a 2-frequency geodesic) and transform the middle triangle into the base of a tetrahedron. Kepler's Stella Octangula is just a K-stellated tetrahedron. K-stellation can only be done to regular polyhedra (currently).

Also note that this new version uses a different method for stellation. The percentage value (the model shown here is 100%) is the relationship between the longest pyramid edge length and the longest original face edge.

31 Jan 2006 - Compound stellation of a tetrahedron. Not! Oops... this is a stellated icosahedron. This was also a test of the new tab labelling system, where each tab lists its page (useful for keeping track of precut pieces) and the face name and page number of the tab it connects to. We need an option for those who prefer the jigsaw puzzle assembly method, however..
Click here for slightly larger image

24 Jan 2006 - a 22" diameter 3-frequency geodesic breakdown of an icosahedron, decorated with tacky clipart. I've been using 70# cover stock, which is available at Staples. It is slightly harder to fold but MUCH easier to put together.

I've also found that it's much easier to put together large models in pieces. I put together four shell-like sections, and glued them together at the very end

Here's a basic tetrahedon that has been stellated 300% - meaning that each of the four faces of the tetrahedon (one of the so-called Platonic solids) has been exploded outward into a pyramid such that the height of the pyramid is 3 times the distance from the base epicenter
   
This is a simple icosahedron - a geometric solid each of whose 20 faces is an equilateral triangle. I've decorated it with photos before printing it out.
   
Here's another tetrahedron, which has been stellated twice, once at 100% and then at 25%. Notice the natural curvature that results from the compound stellation. PaperCut marks concave folds and convex folds separately, but it's a little hard to predict what ends up bending in and what ends up bending out when stellation is done more than once.
   

Last but not least, here is an icosahedron broken down into a 2-frequency geodesic (remember R. Buckminster Fuller?) then stellated.

The stellation actually adds to the structural integrity of the geodesic, and is sometimes used in architecture, not just because it looks cool (remember Epcot's trademark "Spaceship Earth") but because the repeating pyramids make the faces stronger.

   
   

 


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