I have that book and I partially recommend it. It's full of fascinating things. But there are parts of it where I found the writing particularly opaque. For instance, where they tried to explain triality for the octonions. —Dan Adam Goucher wrote: ----- On this topic of 4-dimensional rotations, I thoroughly recommend: 'On Quaternions and Octonions' by J. H. Conway and D. A. Smith. Amongst other things, it includes a classification of all finite subgroups of SO(4). -----