After pondering over the github way of doing web pages and how it fits together with the Sphinx generated documentation I have now two clones of the repository in my working directory and can create the pages in the checkout of gh_page with the checkout of the master branch. As a result the Sphinx docs are now available at http://florianfesti.github.io/boxes/html/index.html and are also linked from the github main page.

PS: Still no laser cutter in sight. So the new click on edges are still untested.