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September 14th, 2016, 03:01 PM   #1
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Traffic on regular lattice n-gons, polyhedrons

If a square lattice (of 2d regular lattices) is most efficient for two-dimensional traffic, is a cubic lattice (of 3d regular lattices) most efficient for three-dimensional traffic?
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September 14th, 2016, 09:08 PM   #2
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Do you have your definition/description of what "two-way dimensional traffic" is on a square lattice?

Do you have the criteria for what constitutes certain two-way dimensional traffic having a greater
efficiency than other two-way dimensional traffic, as they relate to a square lattice?

These sound like highly specialized questions of yours.
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September 14th, 2016, 11:54 PM   #3
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"Two-dimensional traffic" takes place on a plane. One may move in any direction allowed by such a square lattice.
__________

This is the best site I could find on the matter:

Grids Are for Squares: 3 Reasons to Consider Alternatives for City Design | Sustainable Cities Collective

They argue that rectangular (with fewer constraints than square) grids are the more simple, however not necessarily efficient for place-to-place travel. Think of our globe, with nearly rectangular areas near the equator, but convex triangular areas toward the poles. For greatest efficiency, one must keep to great circles.
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I believe that rectangular symmetry can manifest the most right-angled configurations and match better with a plane surface. "Three-dimensional traffic," by virtue of its symmetry with rectangles, would share features of them -- simplicity, so-so efficiency, very good fitting, agreeing with other infrastructure etc. 2D and 3D rectangles work well from large to small scale construction.

There is no single approach that can work for practical traffic engineering; one must compromise somehow. Rectangles seem to work well, and they share many qualities with a rectangular cuboid (3D rectangle).
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