Polyhedra obtained from Coxeter groups and quaternions

摘要: We note that all regular and semiregular polytopes in arbitrary dimensions can be obtained from the Coxeter-Dynkin diagrams. The vertices of a or polytope are weights as orbit Coxeter-Weyl group acting on highest weight representing selected irreducible representation Lie group. This paper, particular, deals with determination Platonic Archimedean solids Coxeter diagrams A3, B3, H3 context quaternionic representations root systems groups. use algebraic techniques derivation polyhedra show possessing tetrahedral, octahedral, icosahedral symmetries related to groups H3, respectively. technique leads except two chiral polyhedra, snubcuboctahedr...