[rllbbgqr] Manifold of multiple polyhedra

Start with a collection of polyhedra and connect pairs of faces like edges in a graph.  You can travel through one face and immediately emerge out the connected other face like a portal, typically into another polyhedron.  This is a 3D manifold.  Only congruent faces can be connected, so this takes some effort to design.  Some possible design shortcuts:

• Limit to polyhedra with a small number of face shapes, e.g., to regular polygons, or even just to squares and equilateral triangles.
• Limit to polyhedra which have all faces the same.
• Limit to regular polyhedra.

Previously, on the difficulty of if you can see through an adjacent cell into a cell beyond that.

The connections between polyhedra could be nicely symmetric, e.g., a network of cubes connected as a hypercube (tesseract), or they could be a mess like a maze or labyrinth.  There are no walls that you can run into, but it's still hard to navigate.

If the faces are regular polygons, the connection also has to specify the twist angle.  Things could also become mirror-imaged.

Two spheres (balls) can be connected through their surfaces, but it seems 2 is the max.

The 2D analogue would be fairly easy: polygonal rooms with matched edges.  For design, polygons can typically easily have their edge lengths adjusted, within the constraints of the triangle inequality.