Catalan solids derived from three-dimensional-root systems and quaternions

@article{Koca2010CatalanSD,
title={Catalan solids derived from three-dimensional-root systems and quaternions},
author={M. Koca and N. Koca and R. Koc},
journal={Journal of Mathematical Physics},
year={2010},
volume={51},
pages={043501-043501}
}

Catalan solids are the duals of the Archimedean solids, the vertices of which can be obtained from the Coxeter–Dynkin diagrams A3, B3, and H3 whose simple roots can be represented by quaternions. The respective Weyl groups W(A3), W(B3), and W(H3) acting on the highest weights generate the orbits corresponding to the solids possessing these symmetries. Vertices of the Platonic and Archimedean solids result from the orbits derived from fundamental weights. The Platonic solids are dual to each… CONTINUE READING