Tensegrity Transformation

[dekay5555555]

You do excellent work. Two things. The tetrahedron and the icosahedron are very intimately related. The most obvious connection is that the icosahedron is a snub tetrahedron.

Secondly, the edges of your tetrahedron are in the golden ratio to the edges of the icosahedron. If tetrahedron edge = 1, icosahedron edge = (square root 5-1)/2 =.618033989

[dwyllie]

@dekay5555555 Oh yes. Amazing. :-)

[mikethechang]

nice music.

[theboombody]

Geometry's never been my passion, but I'm glad some people are into it. It's definitely practical.

[jaime99utube]

Buckminster Fuller called this transformation a "jitterbug", because it looks cool and snappy, like the dance move of his day.

You can demonstrate it yourself physically by making a icosahedron with rubber-tube joints. Then, just manipulated it smoothly into a tetrahedron. Great fun at parties.

[dwyllie]

Please, could you show me a jitterbug video? In this animation, the tetrahedron edges (in orange color) become diagonals of the icosahedron. The edges do not have the same size. Does the same happen with the jitterbug toy?

[jaime99utube]

see YouTube videos:

FfViCWntbDQ

and

RMkHNrLAXJU

[dwyllie]

Amazing videos. However, this transformation is not the same. Jitterbug shows Cuboctahedron, Icosahedron, Octahedron. My animation shows Tetrahedron, Icosahedron.

[dwyllie]

Fuller got the tetrahedron but in a totally different way. Take a look at my video response.

[PrometheusSD7]

I think I'm trippin'

[Italian0z]

nice vid, =) but what's the title of the song? :) thx

[Russellbeta]

ah, so these are built using projection just like you would on a piece of paper? impressive stuff.

[dwyllie]

Yes, more and less.

[Russellbeta]

what software did you use?

thx :)

[dwyllie]

Well, The Geometer's Sketchpad 4. In fact, I implemented the 3D projection because the software has only 2D primitives.