# Scaling Polyhedra

If you use one bar for each edge of a polyhedron, there are usually two sizes you can create it in: short and long. If you want to make your polyhedron larger, you have to use more than one bar per edge. Here I'll discuss three approaches to this.

## Connecting bars via spheres

The most obvious way is to use more than one bar per edge and to connect the bars via spheres in a string. This creates the problem that in addition to the faces not being stable, the edges themselves are not stable anymore, so that, for example, a triangle, which requires no stabilization if built with only one bar per edge, now must be stabilized. In the case of triangles, this turns out to be relatively easy, as this tetrahedron shows:

Fortunately, when stabilizing non-triagonal faces, the resultant polygons are in most cases again triangles, and those can be stabilized easily, like in this dodecahedron:

In some cases it's also possible to stabilize the polyhedron from within, in addition to, or instead of, stabilizing the edges. This is a cube with inner stabilization:

Note that without the inner stabilization, the cube would not be stable. It is also possible to stabilize this cube by using short 4-stars for the edges, in addition to the blue long bars. Then, the inner stabilization would not be necessary.

## Connecting bars directly

You don't have to always connect bars via spheres. They can also be connected directly, as this oversized tetrahedron shows:

Note that when you use this approach, structures which use both short and long bars may not scale up without some redesign, because the ratio in length between a short bar and a long bar with spheres attached is not the same as between two short bars and two long bars with spheres. In other words: While you can build a right triangle with a long bar, two short bars, and three spheres, you cannot do so if you double the bars in length.

## Using larger structures

One can also use more complex structures for edges. This is a dodecahedron for which I have used a bridge-like structure instead of a "thin" edge. Notice that a vertex is now no longer a single sphere, but a triangle:

During the construction I had to support the pentagons with long 5-stars to keep the thing from falling apart. Even after I removed the support when it was finished, it threatened to collapse under its own weight. With the support, it was very stable, though.

## Combining approaches

Of course, you can also use combinations of the approaches outlined above. This, for example, is an icosahedron with each edge consisting of two pairs of two short bars, connected by a sphere: