Discrete Hopf Fibrations

This gallery shows polar orbit polytopes for the cyclic-type tubical groups with all choices of special starting points. It is based on the article Towards a Geometric Understanding of the 4-Dimensional Point Groups by Laith Rastanawi and Günter Rote.

The main goal of the gallery is to show cell decomposition of these polytopes into tubes (discrete Hopf fibrations), and how these tubes are structured and interact with each other.

Screenshots

Running

You can view the gallery live here. Alternatively you can run it independently:

• Clone this repository:

  git clone https://github.com/LaisRast/discrete-hopf-fibrations.git
  

• Generate tubes data (~75.8MiB) by running the script generate_tubes.sage which you can find here:

  sage generate_tubes.sage
  

  Note that this is a Sage script, and you need to install the Normaliz backend to run it. The script will generate the data and put them in data/ directory. Copy that directory into the cloned repository.

• Generate the file files.json:

  python3 generate_file_list.py
  

• Run a local server in the cloned repository:

  python3 -m http.server
  

  and access the gallery through http://0.0.0.0:8000/.

Used Libraries

• RainbowVis-JS: A JavaScript library for colour data visualization. [EPL-1.0]

• three.js: A JavaScript 3D library. [MIT]

• Pico.css: Minimal CSS Framework for semantic HTML. [MIT]