Saturday, March 29, 2008

Mobile Polyhedra

kw: mobiles, polyhedra, geometry

Some months ago a young friend showed me how to make the origami modules for a novel kind of dodecahedron. It has a slightly stellated look, but is not a stellated solid. After some thought, I figured out how to make a number of other polyhedra. The original module has the appropriate angles for the dodecahedron and other shapes that use about thirty modules, but I had to modify it for other shapes with different numbers of modules.

After several months of fooling around I had nine polyhedra of various kinds, some a solid color and some multicolor. I decided to construct a mobile. The backdrop for this image was several black plastic bags. I'll have to get some dark cloth if I want to do any more pics like this. The mobile consists of two smaller mobiles connected by a three-foot rod. Since this image was taken I have replaced the long rod with one of larger diameter that doesn't sag as much. That keeps the whole thing within a foot of the ceiling, making it suitable for hanging in my office (this is my basement workshop).

The larger sub-mobile consists of the original green dodecahedron (30 modules), a lavendar icosahedron (also 30), a pink rhombic dodecahedron (24), a light blue icosadodecahedron (60) and a dark blue rhombic triacontahedron (60).

The smaller sub-mobile consists of a yellow icosahedron (30, smaller modules), a cuboctahedron (24), a shape I think is a snub cube (48) and a darker-hued icosadodecahedron (60). The latter took the most planning, to get each planar section a single color. Purists put these together with friction only. These are glued for durability.

Once I make the appropriate drawings I'll submit a post with directions for the modules and information about making some of the shapes.

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