More fun than a hypercube of monkeys

This model is featured in figure 3.31 of [Visualizing Mathematics with 3D Printing](http://3dprintmath.com).

This sculpture was inspired by a question of [Vi Hart](http://www.youtube.com/user/Vihart). As far as we know, this is the first sculpture (in fact, physical object) with the quaternion group as its symmetry group. The quaternion group {1,i,j,k,-1,-i,-j,-k} is not a subgroup of the symmetries of 3D space, but it is very naturally a subgroup of the symmetries of 4D space. The monkey wa