This Demonstration shows four-point touching families of squares, where . The parameter determines the point by , where is the radius vector of a point . This generalizes , where . In this Demonstration you can vary within an appropriate range to maintain four-point touching in a family with .
A family is said to be -touching provided each element of has a nonempty intersection with precisely other elements of . A -touching family is said to be point--touching if any two touching sets have only a single common point .
Grünbaum has shown that example (with dihedral symmetry) in  is impossible. He has also said that it is not clear whether there are any point-4-touching families with fewer than 48 squares.