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It is well known that the point group of the root lattice D6 admits the icosahedral group as a maximal subgroup. The generators of the icosahedral group H3, its roots and weights are determined in terms of those of D6. Platonic and Archimedean solids possessing icosahedral symmetry have been obtained by projections of the sets of lattice vectors of D6 determined by a pair of integers (m1, m2) in most cases, either both even or both odd. Vertices of the Danzer's ABCK tetrahedra are determined asarXiv:2003.13449v2 fatcat:wz75e7iolvbmzipymylcsu467e