These slides show the limit set of the reflection group studied in my paper with S. Kerckhoff "From the 24-cell to the cuboctahedron". Click "Start" to begin. It is built as follows: take the hyperbolic right-angled 24 cell, remove a certain octet of pairwise disjoint (or tangent) walls, and take the reflection group generated by the remaining 16 walls. The quotient is an infinite volume hyperbolic 4-orbifold. The convex core is finite volume with totally geodesic boundary. The picture has removed an outermost sphere containing all the others. The limit set is the points contained inside the (omitted) outermost sphere but outside all the other spheres. As before, the picture is incomplete. There should be an infinite number of tiny tangent spheres nearly filling the outermost sphere. Preparing the final picture involved computing radii and positions for almost 2 million spheres.
The individual image (png) files can be downloaded either as a Windows zip file or as a gzipped tarball. Also, large versions of the same images can be downloaded either as a Windows zip file or as a gzipped tarball.
The picture was made in 2009 using Sage and POV-Ray.
Take me back to Pete's homepage. Take me back to the image gallery.