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.

See these Mathematica notebooks here and here for a more detailed look at the analysis of the Koca papers used to produce the results :

*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**.*