Balanced six-sided dice

A die comprising:

• a cubical body provided with a corresponding set of five indicia on each face, wherein:
• four of the five indicia of each set form a square pattern with a fifth of the indicia being positioned at a center of the corresponding face, the indicia being distinguishable by colors to represent a first subset of the indicia that are to be counted and a second subset of the indicia that are not to be counted;
• the square pattern of all faces oriented 45 degrees from parallel to the edge of each face such that the die exhibits symmetric weight distribution with respect to each of four space diagonals, each of the four space diagonals extending from a vertex of the cubical body through a center of the cubical body to an opposing vertex, such that weight distributed along one side of each of the space diagonals from the center of the cubical body is balanced by weight distributed along a corresponding opposing side of each of the space diagonals;
• and
• the die exhibits symmetric weight distribution with respect to each of three central axes, each of the three central axes extending through the center of the cubical body, such that weight distributed along each side of the cubic body is balanced by weight distributed along a corresponding opposing side of each of the three central axes.