  We present an explicit algorithm for tessellating the algebraic surfaces
(real 4-manifolds) F(n) embedded in CP3 defined by the equation z0^n + z1^n +
z2^n + z3^n = 0 in the standard homogeneous coordinates [z0, z1, z2, z3], where
n is any positive integer. Note that F(4) in particular is a K3 surface. Our
tessellation contains a minimal number of vertices, namely the n-th roots of
unity in the six standard projective lines CP1 in CP3, which form an obvious
framework for constructing a natural tessellation of F(n). Our tessellation is
invariant under the action of the obvious isomorphism group of F(n) induced by
permutations and phase multiplications of the coordinates, and the action is
transitive on the set of 4-cells. The tessellation is built upon a similar
triangulation for the corresponding algebraic curves in CP2.
