Maybe. It depends a lot on what you're building and what the bricks are doing (supporting a roof, lining a garden bed, building a small rocket cookstove).
Are you wanting to use mortar with these bricks?
The 'right' side of the brick usually has a frog (or whatever the modern term for it is now - it was called a frog back in the 1930s) for the brick to grab hold of the mortar. I'm over simplifying it, based on what I learned from my grandfather who spent 50 years as a bricklayer. I'm sure someone with more technical know-how will chime in soon. This frog was a hollow (sometimes shaped like a frog - but normally an indent, now a days I think it is holes) that made the wall or construction much stronger than a simple flat brick would do.
It doesn't mean you cannot put the brick on its side. If what you are building is small, or you are doing decorative work, it should be possible. If you are building something that needs to meet an official code or has any load barring on it, it might not be the best idea. Or maybe there are ways around it.
I'm doing a fireplace build and am at a point where the flue is being installed and the only way to maintain the outside diameter is to turn the brick sideways. I'm going to go for it and put a lot of brick ties in to keep it sound. Anymore advice on the subject?
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