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September 14th, 2016, 03:01 PM  #1 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 404 Thanks: 27 Math Focus: Number theory  Traffic on regular lattice ngons, polyhedrons
If a square lattice (of 2d regular lattices) is most efficient for twodimensional traffic, is a cubic lattice (of 3d regular lattices) most efficient for threedimensional traffic?

September 14th, 2016, 09:08 PM  #2 
Banned Camp Joined: Jun 2014 From: Earth Posts: 945 Thanks: 191 
Do you have your definition/description of what "twoway dimensional traffic" is on a square lattice? Do you have the criteria for what constitutes certain twoway dimensional traffic having a greater efficiency than other twoway dimensional traffic, as they relate to a square lattice? These sound like highly specialized questions of yours. 
September 14th, 2016, 11:54 PM  #3 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 404 Thanks: 27 Math Focus: Number theory 
"Twodimensional 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 placetoplace 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. __________ I believe that rectangular symmetry can manifest the most rightangled configurations and match better with a plane surface. "Threedimensional traffic," by virtue of its symmetry with rectangles, would share features of them  simplicity, soso 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). 

Tags 
lattice, ngon, ngons, polyhedron, polyhedrons, regular, traffic 
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