find several point make the distance between side of each square and each point, the distance between each point maximum

find several point make the distance between side of each square and each
point, the distance between each point maximum

Each vertex coordinates of the square are (0,0), (1,0), (1,1), (0,1),
Inside the square, find a point make the distance between side of each
square and each point, the distance between each point maximum, obvious
the coordinates is (1/2,1/2).
if require find two point or more, What are the coordinates of these points?