An Icosahedral Tensegrity Study using multiple vZome viewers.
I finally got around to modeling one of my favorite physical zometool designs in vZome. I realize that it’s not really a tensegrity model as shown here, but I think the red struts could be held in place with strings in a way that makes the other struts unnecessary. Some day I may try it.
Yes, this design can be constructed completely from real zometool parts. It features 30 non-intersecting red lines with icosahedral symmetry and several options for scaffolding struts to hold them all in position.
Each red “line” consists of 4 collinear struts connected end-to end. Groups of five of these parallel lines form the edges of regular pentagonal prisms. Six of these prisms centered on the origin are the basis of the whole design.
An interesting property of this design is the pentagonal prisms through the origin whereas most shapes with icosahedral symmetry, like the dodecahedron, have antiprisms through their centers.
Since the red struts don’t intersect, we can use blue, yellow or green struts as scaffolding to hold them in place. Any one type of strut is adequate. I’ll show all three posibilities below. The downloadable vZome model has individual bookmarks that correspond to the various scaffolding configurations shown here.
Using yellow scaffolding only.
Blue scaffolding forms the vertices of an icosahedron. Note that the red lines are not on any faces of the icosahedron.
Green struts can be used as scaffolding at the tips of each red line.
This design shows all of the scaffolding combined in one model.
All of these models can also be combined in a single viewer.