@mathzorro the way lattice paths occur in the 'reflectome' of a cube here, marked by parity (odd segments in the 'unreflected'-reflected , even segments in 'reflected'-reflected) is quirky
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To based on a design for a physical object dodecahedron with one way mirror for faces and bright edges
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I meant in more of a pure mathematics context: if we are seeing not-lattices, then what sort of not lattices are we seeing?
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Over complete?
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each cell is a reflection. except for the cubical case, (which is a strange, fidgety lacquer on Z^3), the spaces formed are not hyperbolic. They are reminiscent of the Poincare homology three-sphere, but with halls of mirrors
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