Actually On the Subject of 4×4×4 Sudoku

You think he’d learn his lesson on making puzzle modules with ambiguous solutions. Now, he’s making nerfed versions of another module, and still hasn’t learned his lesson.

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

Each row, column, stack, and 2×2 squares projected from the X, Y, and Z planes of the cube 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, in addition to the M selector.
The M selector will display 2D projections of the provided plane from the cube provided, by omitting projections of the X, Y, or Z axis.

If the selected cell is empty, a white sphere will be 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.
An incorrect solid placed an empty cell can be overridden by selecting another solid or cleared by selecting the highlighted solid. Cells whose solids have a gray highlight CANNOT be overridden nor cleared.
To reset the entire module to the beginning, hold any of the solids for around 2 seconds on a cell without a gray outline.

The module is solved once all cells are correctly filled.