Cube Dimensions Analysis: Comparing Height and Length Properties

To determine whether a cube can have a height that is different from its length, we must recall the definition of a cube.

A cube is a special type of three-dimensional geometric shape wherein all the sides are equal in length. In mathematical terms, if a cube has a side length of $a$, then its dimensions are $a \times a \times a$. This means the length, width, and height are identical.

Since the height and length of a cube are both represented by the same variable, since their definitions require that they are exactly the same length, a cube cannot have a height that is different from its length.

Therefore, according to the geometric properties that define a cube, the height cannot be different from its length.

Thus, the answer to the question "Can a cube have a height that is different to its length?" is No.