The two basic equations satisfied by the parameters of a block design define
a three-dimensional affine variety D in R5. A point
of D that is not in some sense trivial lies on four lines lying in
D. These lines provide a degree of organization for certain general
classes of designs, and the paper is devoted to exploring properties of the
lines. Several examples of families of designs that seem naturally to follow
the lines are presented.Comment: 16 page