Welcome to the Pentadome

This thread on Boardgamegeek has a very cool discussion of the kind of grids that can be had by tiling pentagonal shapes, as opposed to the usual 4 or 6 sided figures.

The limitations of pentagons as a general spatial simulation soon become evident. But if you have a truly alien dungeon, building complex, or spaceship to show, there'd be nothing to make your players' eyes bug out like mapping it on this kind of paper: