Are Triangles a Better 'Divisor' of a Battlefield than Hexes?

Phil's Diagram of Triangular Tiling

Yesterday, I read this post by Phil and the subsequent discussion; they prompted some thoughts.  Phil reported on further developments here.

Triangles might work well if stands are placed on the points rather than in each triangle. Each point can be perceived as the centre of one hex and the point of 6 hexes and each hex overlaps 6 other hexes as illustrated in the next diagram.

Each hex overlaps 6 other hexes

A distance of 2 points for movement and distant-combat is equivalent to 1 hex so conversion of rules intended for hexes may be straight-forward.

Reasons why I like hexes are explained here. I've yet to work-out whether points of triangles and hexes that overlap are a useful construct and hope one day to make the time to experiment with it. 

One such experiment might involve a unit of 3 stands. For example, the unit could comfortably wheel around one hex as illustrated here.

A unit of three stands wheels to the right