There only two main types of tiling for tbs - squares and hexes, and both have problems. hexes dont have all 4 straight moves, its look so painful to watch how units move left/right in civ5, they really describe half arc. squares have all 4 straight lines and 4 diagonal, but they dont geometrically correct, like in civ3 if you explore diagonally then you open twice as much tiles. so, how we can have both properties, all movement and geometric correctness? there are bunch of solutions that i come up with. 1) change cost of diagonal movement on square grid, possible solutions are: 2; 1,5; 17 if straight cost 12. maybe it good enough for tactics, but for strategy not so much. if unit have one movement than it has to move regardless of direction, unused ap is bad. 2) allow in hexes grid movement also to vertices, thereby doubles directions. +all 4 straight moves, +diagonals, -movements are not geometrically correct, some cost 2 some root(3), -not true diagonal, - 6 way to move from hex to vertex, but only 3 to come out. also how to draw map? 3)tessellation with gaps. you can use concentric rings to construct tessellation with any regular polygon, idea from hyperbolic geometry. + as many direction of movements as you like, -0 correctness. so, any more ideas?