grid - Why don't we use octogonal maps instead of hexagonal maps?

I understand the advantage of hexagonal tiles over square ones. But why aren't octagons used instead? I would think they would provide better, more natural movement in eight directions.

I was thinking about using that kind of map in some game, but I haven't seen any games using it, so I wonder if I missed something obviously flawed about using it?

Answer

Octogons:

Hexagons:

The gaps in the octogons make for an unappealing game world.

Typically, if you wanted to allow for eight directions of movement, you would just use squares.