On the Subject of Latin Hypercubes

Tolle rationem deductionis ad altiorem tuum dimensionem.

On this module is a 4×4×4×4 grid. Each cell may contain one of four solids: Tetrahedron, Hexahedron, Octahedron, or Dodecahedron.

Each row, column, stack, and rank of the grid may only contain one of each shape.
There is only one arrangement of solids that fits within the constraints with the given starting configuration.

Navigate around the cube using the four buttons at the top of the module.
Pressing any one will move the cell selector one space in its direction, wrapping around if it exits the grid.
The coordinates of the selector are shown on the buttons.
Only solids with the same W coordinate as the selector are visible on the module.

If the selected cell is empty, a white sphere is visible inside it,
otherwise the button with the solid in the selected cell will be highlighted.
Pressing one of the four buttons to the right of the module will place its corresponding solid in the selected empty cell.
Placing the wrong solid in an empty cell will incur a strike.

The module is solved once more than two thirds of the cells are filled.