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Triangle is the most stable polygon in geometry. I'm wondering why then the building bricks are all rectangular, not triangular?

You still have the problem that each white brick is trying to push two blue bricks apart. Wet mortar is very weak in shear or tension. If you offset courses you will be supporting the whole of a blue brick on the point of the one below it, whereas rectangular bricks distribute the compressive load evenly over the entire block.

So what if we compare triangular bricks and traditional bricks in lab? Do you all think it would be a good project?

I love this thread. ... Walls need to turn corners and are supported by piers. I do not see any way a triangular brick can do this. Nor can a cubic one. The rectangular brick with one side twice the other was found about 5,000 years ago to be the best way to tie a wall around a right angled corner and remains so to this day.