Balloon Hyperbolic Planes

Balloons are a great medium for making large hyperbolic planes. These constructions are modular, and it is quite tempting to keep making and adding modules, to see the model's hyperbolic nature take shape. It also is a good model to construct with friends, for this reason!

There are many possible tilings to choose from, most of which have never been made out of balloons (or perhaps anything else, for that matter). The wikipedia page is a great reference.

The above plane is based on tiling seven triangles around each point. Each balloon is twisted into 7 sections, which is computationally efficient.

Another nice tiling is four pentagons around each point. In this model, I used one balloon for each "straight" line.

I like this next tiling for the lovely star-like modules that are possible. Because each balloon is twisted into 12 sections, the finished product ends up very smooth and dense.

The following snub hyperbolic tilings can be made out of the snub modules described on the snub balloon polyhedra page. The modules are easy to make and connect, making these especially good for groups.

When your hyperbolic plane is all put together, the balloons can usually use some shifting to make them flat and even at the vertices, and show off its hyperbolicness.