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[hudders]

Hexagons will tessellate around a central pentagon which looks pretty nice.

[Russell.s]

I like hexagons/octagons too

I was experimenting with decorating them a bit though, trying to get more interesting shapes. Unfortunately I can't make an entire fortress look like that, because of terrain and mineral features...

So here are my dining room and barracks:

They look great! I tend to shy away from open spaces in my forts, but there's no reason I couldn't just remove the internal walls of any tessellating pattern to create larger spaces.

I also never really bother following mineral veins... am I a bad dwarf?

[ASCIt]

I've always enjoyed a tessellating pattern for my bedrooms. It goes a bit like...

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[W][W][W][X][W][W][W]
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[Itnetlolor]

If you want to fit infrastructure without interrupting the flow of the build, you can always go for the soccer ball (football) formation combining octagons and squares in sequential pattern. You can make use of the un-mined cells to fit the machinery and watrer/magma pipelines through. Sure, there may be some wasted space with this method, but the square cells can also double as blast doors or airlocks of sorts. Just a thought.

Triangular patterns in manner like this: ▲▼▲▼▲▼▲▼▲▼ can also serve a decent, yet efficient, purpose (with or without diagonal or horizontal hallways (vertical if rotated 90°)). Triangular can also be adapted to form hexagon patterns with a central doorway as a shortcut between cells (or as a method of quarantine) or as a common well/drinking zone.
Tri-Hex example:
▲▼▲
▼▲▼

You can also do Tetris-style construction/mining. However, to add to the challenge, quarantine any sections that form a full line. And by God, don't get a full Tetris (4 lines in a row).

One last pattern to work with is the X-Com Base build. Extra points if you also make them look just like the bases in-game. More extra points if you can make a carbon-copy replica of the starting base build.

One last pattern idea: Stained glass. Build a stained glass image with your fort (better if constructed for color accuracy, I suppose; no engraving unfortunately). Design something, and use geometric shapes to build it with corresponding colors.

Alternatively, you can always go the Tangram route.

Spoiler: examples (click to show/hide)

Granted a good rule of thumb with Tangram construction/mining is that it must stay true to the game/puzzle, and use only the pieces given per-fort section/accessible floor. Should make for some interesting builds, and fun base designs.

EDIT:
Interesting thought about the tangram route. You can build specialized mini-forts or assigned burrows according to the pattern designed. Something to consider whenever burrows work better.