I wanted to rotate $\Box$ $45^\circ$ clockwise to make a diamond. At the time, I did not know there was a diamond command $\diamond$ and $\Diamond$ and $\diamondsuit$ and even things like $\not\diamondsuit$. But I then wondered to myself, is there a command to rotate symbols? For instance, say I had the letter $\Psi$. I can rotate this, only $180^\circ$ but not with some fancy rotating command. Simply, I use \pitchfork and this generates $\pitchfork$. A bit like a flip. I can also flip curved lines. For instance, take the curve $\frown$. I can flip it $180^\circ$ but with an entirely seperate command, \smile to generate $\smile$.
The examples that I mentioned however, are only certain examples where I can flip them. For example, I can flip arrows. $\downarrow$ $\leftarrow$ $\uparrow$ $\rightarrow$ $\wedge$ $>$ $\lor$ $<$, but none of these uses a rotating command; only directions. But say I want to flip the curve $\smile$ only $90^\circ$. Then how would I do that? I can write the command, \between but this generates $\between$ which is both curves flipped $90^\circ$, not one. I would simply have to use brackets $()$. And if I wanted to rotate a symbol like $\gtrless$ then what command do I use now? I would have to use two commands to generate $\land\lor$ and $\lor\land$ but I won't be able to flip $\gtrless$ sideways.
Essentially, I am asking if there is some kind of rotating command, and if not, is it ok to feature some kind of command like that?
Thank you in advance.