A square is a two-dimensional mathematical and graphical representation with four sides, all 4 of equal length, and having equal angles at all 4 of its vertices, 90 degrees.
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Move two adjacent coins, leaving the other pair of adjacent coins untouched. Place them on opposite sides of the unmoved pair, so that they become diagonally opposite corners of the new square.
define a subset
It depends on what you define as a "square". If you are talking about the faces of the cube, then there are 6. If you are talking about actual squares, then there is no answer without specifying the size of the squares and the size of the cube and possibly other factors.
define or describe each set of real numbers?
The two foci are necessary to define the location of an ellipse, but the shape depends on the eccentricity, which is related to the lengths of the two axes.