Balanced six-sided dice

A die comprising:

• a cubical body provided with a corresponding set of seven indicia on each face, wherein:
• six of the seven indicia of each set form a regular hexagon pattern with a seventh 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;
• a first face and a second face of the body have a first edge located therebetween;
• the hexagon pattern of the first face is oriented such that a first side of the hexagon pattern of the first face is oriented substantially parallel to the first edge;
• and
• the hexagon pattern of the second face is oriented such that a first indicia of the hexagon pattern of the second face is oriented nearest the first edge at a midpoint of the first edge and of the first side of the hexagon pattern of the first 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.