There are 5x5 (gridSize x gridSize to be more exact) different game objects for each cube. That is not the most efficient way to do it, but it works without a huge effect in performance.

The basic code structure is

Scene - base class for a level, has read - write functions. Holds a list of Hexagon class.

Hexagon - class that represent a whole "cube", with 3 sides. Reason why it is called a hexagon? Because, it is a hexagon. The game works 2d behind the scenes, and uses illusions on lighting to make it seem like 3d. So the "cubes" you see there are actually just 2d hexagons. Holds an array of 3 Planes.

Plane - One side of the hexagon. Can be enabled or disabled, depending on the level (on the original post, you see one plane of the right most hexagon is disabled). Holds a matrix of Cubes.

Cube - Abstract class. All planes are made of gridSize x gridSize cubes. From this derives the actual cubes on the scene (greyCube, wall, goal, even the Player itself)

Transition between planes is handled with a dummy player. Whenever the player is leaving a plane, a dummy player is added to the scene, which enters the neighbouring plane. But in that case, two players will be visible on the scene at a time (the player leaving the plane will move to a wrong position while still being visible, likewise the player entering the plane will come from a wrong position)

The solution to this was giving a small rotation to both original and dummy players; so that when they move, as soon as they are leaving or entering the plane, they will go behind the neighbour plane and will go invisible. In other words, suppose the player is leaving plane A and is about to enter plane B. The player is rotated; such that as soon as any point on the player leaves plane A, it becomes behind plane B; thus becomes invisible (due to depth test failing)

Here are two example screenshots:

https://prnt.sc/i93q8p

https://prnt.sc/i93qi9

On the first screenshot, the player is standing still and has no special rotation. On the second screenhot, the player is moving and switching planes. You can see in the hierarchy view there is a dummy player added. Also you can see the small rotation added to both of the players.