About three years ago, I wrote an article
on my blog about Ungar’s approach to hyperbolic geometry, and how it
can be used to draw some hyperbolic polyhedra in R, using the
**rgl** package. I invite you to take a look at this
article.

Now I’ve implemented these ideas in the **gyro**
package. Maybe you know there are several models of hyperbolic geometry;
**gyro** deals with the hyperboloid model (or Minkowski
model) and the Poincaré model.

The main functions of the **gyro** package dealing with
3D polyhedra are:

`gyrotube`

, to draw a tubular hyperbolic segment (if you don’t want a tube, use`gyrosegment`

instead);`gyrotriangle`

, to draw a filled hyperbolic triangle in the 3D space;`plotGyrohull3d`

, to draw the hyperbolic convex hull of a set of 3D points.

You can run `gyrodemos()`

to get some examples of code
which draw some hyperbolic polyhedra.

If you are looking for other polyhedra, you can go to the
**Visual Polyhedra** page of the dmccooey website.
Here you will find the Cartesian coordinates of the vertices of many
polyhedra. If the polyhedron is convex (in the Euclidean space), use
`plotGyrohull3d`

to quickly draw it. Otherwise you need to
know the faces of the polyhedron, and they are given on the dmccooey website.
From the faces you can derive the edges. See `gyrodemos()`

for some examples. The eusebeia website is another
resource to find the Cartesian coordinates of the vertices of some
polyhedra. Finally you can also use the R package Rpolyhedra.

The **gyro** package also offers the `tiling`

function to plot hyperbolic tilings of the Poincaré disk.