I'm sure you know the baby game about sorting shapes by putting them in holes:
I'm wondering if such a game could exist in 4 dimensions? I imagine the shapes would have 4 dimensions and the holes 3 dimensions...
Essentially what you need is a cross-section of a 4D polytope, representing a hole through which it can pass. These cross-sections can be quite complex. For example, the great icosahedral 120-cell, a regular star 4-polytope,