The regular hexahedron or cube is the only regular solid that self associates to completely fill space with each cube having a contact relationship with 26 adjacent cubes - 6 in face contact, 12 in edge contact and 8 in vertex contact.

The general perception of a cube is that it is a solid object in space and therefore rigid and unchangeable. This is not the case if the cubes in an infinite array are considered as cells of space, each defined by eight vertex points.

The eight vertices are equivalent to mathematical points with each vertex having zero dimension. An infinite number of other vertices can therefore be superimposed on a given vertex point without any apparent change to the condition of the given point.

Two adjacent points define line segments with a single dimension - length.

Four adjacent points define polygonal faces with two dimensions - length and breadth.

In each case an infinite number of identical lines and polygons can be exactly superimposed without any apparent change of condition.

For the sake of familiarity & understanding the transformations shown will be referenced to and from a cubic state.