Compression and Tension are good; Torque's a Killer

Plato, Fuller and the three little pigs   (continued)

This is a work in progress. Some of the tension bearing members, the red tinted 'rubber bands', are drawn improperly (in the foreground) when they should be behind, and occluded, by the rods.

This is not a raytraced image. Raytraced images are drawn one pixel at time, which is a relatively slow process. Since all the objects in the image are bounded by flat surfaces, and the number of surfaces is much smaller than the number of pixels in the image, it is much faster to construct the image by drawing fewer, larger polygons, rather than the more numerous pixels one at a time. This object was drawn using polygons, and it took only a second or two on my little '486 (a processor that was considered fast a few years ago).

Some faceted objects are easier to draw than others. Convex objects, those having no concavities (indentations), such as the the Platonic solids, are easier to draw than concave objects. In other worlds, if you wrote a little program to draw convex objects quickly, and then forced it draw some thing more complicated, well you might get an image renderedly improperly, like the image above. (Notice I didn't use the 'B-word' in describing the programs performance).

The neat thing about this though, is the program spins the web of conecting strings on the fly. The data set for the whole image is as follows:

static Vector fuller[6][2] = 	{	
	Vector(  0,  1,  0  ),  Vector(  1,  0, 0 ),	
	Vector(  0, -1,  0  ),  Vector(  1,  0, 0 ),
	Vector(  1,  0,  0  ),  Vector(  0,  0, 1 ),	
	Vector( -1,  0,  0  ),  Vector(  0,  0, 1 ),
	Vector(  0,  0,  1  ),  Vector(  0,  1, 0 ),
	Vector(  0,  0, -1  ),  Vector(  0,  1, 0 )
    };

Two views of our friend the Dodecahedron. But why are they here?

The Dodecahedron has 12 sides, and for each side, there is an opposite face, parallel to the first. However, when we look at a "wire mesh" version of the dodecahedron and we have an edge rather than a face pointing directly at us, another symetry becomes apparent. Now two faces are facing us equally (though not squarely), and we see straight through, with no obstructions at all, looking through a second pair of similarly aligned faces. With a little bit of imagination, this is like staring down the barrels of a double barrelled shot gun.

We could easily place a pair of parallel cylinders into the four holes formed by the four open faces of the wire mesh dodecahedron and they would lay parallel and astride of the center of dodecahedron. We could place a total of 6 cylinders, pairs in parallel, each pair perpindicular to every other, filling every hole, and giving every cylinder exactly one entry and exit hole. What would that look like? Well that's where be began.

A related topic: The Platonic Solids: The dodecahedron and the rest.

A comercial kit: Tensegritoy No graphics discussion, but if you want to build one from a kit...