In this description,* (8,1) consists of the roots with permutations of (1,−1,0) in the last three dimensions, together with the Cartan generator corresponding to the last two dimensions;* (1,78) consists of all roots with (0,0,0), (−½,−½,−½) or (½,½,½) in the last three dimensions, together with the Cartan generators corresponding to the first six dimensions;* (3,27) consists of all roots with permutations of (1,0,0), (1,1,0) or (−½,½,½) in the last three dimensions.
* The (1,78) consists of all roots with (0,0,0), (−1/2,−1/2,−1/2) or (1/2,1/2,1/2) in the last three dimensions, together with the Cartan generators corresponding to the first 6 dimensions.