whatever repeating Patterns are: Equalateral Triangles (6-way intersections), squares (grid) (4-way intersections), and regular hexagons (3-way intersections)…..

Personally, I think it is a 6-way intersection, because in a repeated pattern of equalateral triangles, to illistrate this you can use the east-west streets and then 60 degrees northerly of West, northerly of East, and 60 degrees southward of West, southward of easterly — this repeated pattern goes in the most directions (cuts distances), but the move at each intersection is longer. Currently the most popular, is the 4-way intersection, squares. This seems reasonable. And the 3-way intersection, regular hexagons has the least move at each intersection, but you lose efficicency for individual distances traveled.

Which way is best? And why arent 6-way intersections the most popular choice? It is Mathematically, correct, right?!

Note: you cant have solon than 6 i think, because no repeating pattern exists that is the same throughout.