Integrable top equations associated with projective geometry over Z2

We give a series of integrable top equations associated with the projective geometry over Z(2) as a (2(n) - 1)-dimensional generalization of the three-dimensional Euler top equations. The general solution of the (2(n) - I)-dimensional top is shown to be given by an integration over a Riemann surface with genus (2(n-1) - 1)(2).