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Rotating a letter

For a work in logic, I need to write a iota upside down in a mathematical formula. I found this suggestion on the internet. First include [the usual math package] and the graphicx package

\usepackage{amsmath, amscd, amsthm, amssymb, mathrsfs,amsfonts}
\usepackage{graphicx}

in the preamble. Then use the command 

\rotate{180}{$\iota$}

Indeed it works, but not perfectly: the axis of the rotation is at the basis of the letter (in 'normal' position). Hence, when I use this command, the reversed iota appears on a lower level than the text. I am thus not satisfied with this.

Does anyone have a better suggestion?

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Thomas Connor
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2 Answers2

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A reference is Rotating a letter, but rotating math symbols requires some more care:

\rotatebox[origin=c]{180}{$\iota$}}

The $ signs are necessary, since TeX is not in math mode when it processes the contents of the box to be rotated.

If the symbol is needed also in subscripts or superscripts, some more work is needed:

\newcommand{\rotatediota}{{\mathpalette\rotiota\relax}}
\newcommand{\rotiota}[2]{\rotatebox[origin=c]{180}{$#1\iota$}}

Now $\rotatediota_\rotatediota$ will have the desired result (graphicx is required, of course).

Explanation

\mathpalette\XXX\YYY becomes

\mathchoice{\XXX\displaystyle\YYY}{\XXX\textstyle\YYY}
  {\XXX\scriptstyle\YYY}{\XXX\scriptscriptstyle\YYY}

and TeX will choose the right piece of code depending on the current math style. So it suffices to define \XXX with two arguments, the first of which is a math style declaration. Here we don't have a "variable" part, so the second argument to \rotiota is just \relax (it could be any token, since it's eventually discarded; \mathpalette requires two arguments, to begin with).

The extra group around \mathpalette\rotiota\relax is to allow for a simpler syntax when the symbol must be used in a subscript.

If it has to be a relation symbol, don't forget to put it into \mathrel, or modify the definition to

\newcommand{\rotatediota}{\mathrel{\mathpalette\rotiota\relax}}

Remarks

This is also a good candidate for a command to be declared robust, if used extensively in captions or headings:

\DeclareRobustCommand{\rotatediota}{...}

or, loading etoolbox,

\newrobustcmd{\rotatediota}{...}
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egreg
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\reflectbox{$\in$}

You can use a reflectbox as well.

\reflectbox{$\iota$}
daemondave
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    The question is about rotating, not reflecting around the y-axis, which is what \reflectbox does. You can reflect around the x-axis with a combination of \scalebox and \raisebox, though. – egreg Sep 23 '16 at 22:56
  • perhaps you're not aware symmetry about an axis - which is exactly what rotate 180 means. – daemondave Oct 05 '16 at 00:49
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    I know enough math to distinguish between a direct (positive determinant) isometry from an inverse one. A rotation is direct, a reflection is inverse. Try rotating and reflecting a P in order to appreciate the difference. – egreg Oct 05 '16 at 06:08
  • Yet you missed his constant 180, not theta or a variable. He won't care how smart unless you help him with his problem, or not. Your morphisms and mine are equivalent, in the asker's case, up to isomorphism. – daemondave Oct 05 '16 at 17:39
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    No; reflecting or rotating a iota gives different results. – egreg Oct 05 '16 at 17:44
  • No egreg, while you were so busy trying to correct superfluous math you neglected he wanted a transform that worked for this specific case. If you mapped them out the domain to range is bijective for his case. That makes it an answer he can use. That's all he wanted. Not a category lesson. – daemondave Sep 27 '19 at 16:19
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    An image is worth more than a thousand words click here – egreg Sep 27 '19 at 16:32