Click here to view the Powerpoint presentation.
It shows code and output from my VisibLie-E8 tool generating all Platonic, Archimedean and Catalan 3D solids (including known and a few new 4D polychora from my discovery of the E8->H4 folding matrix) from quaternions given their Weyl Orbits.
If you don’t want to use the interactive Powerpoint, here is the PDF version.
- Koca, Mehmet; Ozdes Koca, Nazife; Koc, Ramazon (2010). “Catalan Solids Derived From 3D-Root Systems and Quaternions”. Journal of Mathematical Physics. 51 (4). arXiv:0908.3272. doi:10.1063/1.3356985.
- Koca, Mehmet; Al-Ajmi, Mudhahir; Ozdes Koca, Nazife (2011). “Quaternionic representation of snub 24-cell and its dual polytope derived from E8 root system”. Linear Algebra and Its Applications. 434 (4): 977–989. doi:10.1016/j.laa.2010.10.005. ISSN 0024-3795. S2CID 18278359.