The lattice matching of two sets of quaternionic roots of F4 leads to quaternionic roots of E8 which has a decomposition H4 + σ H4 where the Coxeter graph H4 is represented by the 120 quaternionic elements of the binary icosahedral group. The 30 pure imaginary quaternions constitute the roots of H3 which has a natural extension to H3 + σ H3 describing the root system of the Lie algebra D6. It is noted that there exist three lattices in 6-dimensions whose point group W(D6) admits the icosahedral symmetry H3 as a subgroup, the roots of which describe the mid-points of the edges of an icosahedron. A natural extension of the Coxeter group H2 of order 10 is the Weyl group W(A4) where H2 + σ H2 constitute the root system of the Lie algebra A4. The relevance of these systems to quasicrystals are discussed.
|Number of pages||15|
|Journal||Turkish Journal of Physics|
|Publication status||Published - 1998|
ASJC Scopus subject areas
- Physics and Astronomy(all)