Orb is a computer program that can find hyperbolic structures on a large class of hyperbolic 3-orbifolds and 3-manifolds. It can start with a projection of a graph embedded in the 3-sphere, and produce and simplify a triangulation with some prescribed subgraph as part of the 1-skeleton and the remainder of the graph drilled out. It enables computation of hyperbolic structures on knot complements, graph complements and orbifolds whose underlying space is the 3-sphere minus a finite number of points.
The program was created by Damian Heard by modifying Jeff Weeks' computer program SnapPea. This work was partially supported by an Australian Postgraduate Award and grants from the Australian Research Council.
A new version of Orb is now available which runs on current versions of Mac OS X. A version for Linux is also available.
NEW: Thanks to the efforts of Marc Culler, a precompiled version of Orb that runs on current versions of Mac OS X (10.6 - 10.8) is now available below.
Click the following links to download a precompiled version that should run on Mac OS X (versions 10.3 - 10.5)
NEW: The source code below should compile under Mac OS X and on Linux.
(Thanks to Matthias Görner for getting Orb to compile on Linux.)
The following is a link to Orb's source code:
If you have any questions or comments about Orb, please contact Damian Heard at the e-mail address: Damian 'dot' Heard 'at' gmail 'dotcom'. (Note: the e-mail address is written this way to avoid spam.) A copy of his PhD thesis can be found here. Please note, this pdf file has changed. In the original pdf there were errors in the symmetry groups on pages 71-78.
Department of Mathematics | University of Melbourne