Monday, December 15, 2008

Two More Abstract Models

After building my "Esses" model (see previous post) I set to work on two more "abstract" models (models where the faces interweave without enclosing an area). The first is a model I designed myself that is based on the first stellation of the icosahedron. For those of you who don't know what that means, a stellation of a model is when the faces of a model are extended until they intersect. And if that still makes no sense, what stellation does in practice is make convex (round) polyhedra into stars (from the greek "stella", or "star").
Anyhow, the first stellation of the icosahedron is a pretty dull looking model, which is why I chose it as the subject for an interesting looking abstract model. The model has 20 pinwheel-shaped parts, which is why I chose bright colors to build it with. The way in which they interweave leaves 12 large pentagonal holes (shown below) which I think look pretty neat.

The second model in this post is a paper model I made of a sculpture by George Hart. It's a fairly complex model, so I hope the pictures can at least give you a sense of the thing. It has two parts to it that interweave with each other without actually being glued togother. The core of the model (in light green) is basically a rhombic triacontahedron with sections cut out of the faces. The outer red structure is a stellation of this core, also with sections cut out of the faces.
They each are made of 30 similar-looking parts, which were very difficult to cut out of cardstock! Since the red and green parts of the model interweave but are not held together by glue or tape, they can move around slightly relative to each other. This is an *extremely* delicate model! As you can see by this next image (photos courtesy of Sam Scheidler, by the way), this model also has neat pentagonal holes.

So, there you have it! These are my current most recently completed models (except for a quasitruncated hexahedron, but that was just for fun), but I have lots more on the way. Particularly a great dodecicosidodecahedron in 7 shades of pink and purple. But maybe I'll save that for Valentine's day.

Tuesday, December 2, 2008


A month or so ago I was fooling around on Great Stella, faceting stellations of the rhombic triacontahedron, when I came across this cool shape. It is made up of 30 "S" shaped pieces (or backwards S's, depending on whether you make it left- or right-handed), and they interweave in very interesting ways. The really neat thing about this model is that even though the pieces interweave among eachother quite a bit, they don't actually touch except at the twelve points of the model. Also, each point is not directly connected to any of the points directly next to or across from it; only to points exactly two points away. This was my first "open-faced" model; in other words, it is made up of strips of paper that don't actually have any thickness.

Unfortunately, a few days after building this model I found two other designs similar to it. The first is by Robert Webb, who created the Great Stella program that I like so much. His model is topologically the same, though he made the peices a lot thicker. And the second similar design is the sculpture "Compass Points" by George Hart (the "inside" structure of this model is the same basic shape as mine). Well, it was still fun to build something that I at least thought I had discovered.

Inspired by this model, I have already built two more "open-faced" models. One is a direct copy of a model by George Hart, and the other is my own design (and this time it really is my own). As soon as I can get Sam to photograph them I'll post on them.