  In this paper we classify completely all regular minimal surfaces with K^2=8,
p_g=4 whose canonical map is composed with an involution. We obtain six
unirational families of respective dimensions 28,28,32,33,38,34. The last two
are irreducible components of the moduli space of minimal surfaces with K^2=8,
p_g=4. These families hit three different topological types.
