# HexaCube Math

HexaCube d4s are, like all HexaCube dice, chamfered cubes, a shape which also goes by the impressive name of tetratruncated rhombic dodecahedrons. A chamfered cube is a cube with the edges sliced off to make 12 new faces. This means that a chamfered cube has 18 sides. Six of the sides are square faces. (They are smaller versions of the original cube’s sides). The faces that have replaced the cube’s edges are 12 hexagons. The hexagons can have all the same lengths, or be irregular. HexaCubes use irregular hexagons, with two sides longer than the rest. However, each of the 12 hexagons on a die are exactly the same. To avoid confusion, I refer to these irregular hexagons as “hex faces.”

The key to understanding the theory behind HexaCubes lies in two concepts. The first is that the relative size of the two kinds of faces can be adjusted so that it is more, or less, likely that the die lands on a particular kind of face. For example, if the square faces are made larger in relation to the hex faces, it will become more likely that a rolled die will land with a square face up. The second concept is that manipulating these probabilities can be used to make fair dice that have a different amount of sides than outcomes.