`library(gyro)`

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).

The main functions of the **gyro** package 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. It is archived on CRAN, but you can install it from the `tar.gz`

archive.