240 non-zero roots of E sub 8 are constructed a la Dickson and Coxeter by defining simple roots in terms of octonionic units. They close under subtraction and multiplication. It is noted that the integral octonions of norms 1, 2,...,13 which constitute the dominant weights of unit multiplicity of certain representations of E sub 8 define Gosset's polytope in 8 dimensions. Similar features of integral quaternions forming the SO(8) root lattice are briefly mentioned. 13 references, 3 figures, 1 table. (ERA citation 12:042497)
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