A simple application of \ooalign
:
\documentclass{article}
% Simple version if you don't need it in sub/superscripts
%\newcommand\gdw{\mathrel{\ooalign{$<$\cr$>$\cr}}}
% Fuller version
\makeatletter
\newcommand{\gdw}{\mathrel{\mathpalette\@gdw@\relax}}
\newcommand{\@gdw@}[2]{\ooalign{$\m@th#1<$\cr$\m@th#1>$\cr}}
\makeatother
\begin{document}
$X \gdw Y_{\gdw}$
\end{document}

See this answer for a quick course on \ooalign
. What's the advantage of this complicated looking solution over a seemingly simpler “print >, back up and print <”? That you don't need to guess the width of the symbol, which might change with the font used; with \ooalign
you don't run the risk of having to compute the width.
If you want to make the inner rhombus smaller, you can add some pushing:
\documentclass{article}
\makeatletter
\newcommand{\gdw}{\mathrel{\mathpalette\@gdw@\relax}}
\newcommand{\@gdw@}[2]{%
\ooalign{$\m@th#1\@gdw@push<$\cr$\m@th#1>\@gdw@push$\cr}}
\newcommand{\@gdw@push}{\mkern2mu}% adjust to suit
\makeatother
\begin{document}
$X \gdw Y_{\gdw}$
\end{document}

Another possibility:
\documentclass{article}
\usepackage{mathtools}
\newcommand{\gdw}{%
\mathrel{\mathrlap{>}}% print > with zero width
\mathrel{\mkern2mu}% some small spacing
<% print the <
}
\begin{document}
$X \gdw Y_{\gdw}$
\end{document}
This produces exactly the same output as the last one (with the 2mu to be adjusted to suit). It is simpler in its aspect, because it uses \mathpalette
internally. It exploits the fact that TeX inserts no space between consecutive relation atoms.
\iff
? BTW, I've never seen that symbol before. – Henri Menke Dec 12 '14 at 21:58\leftrightarrow
would be used. – Jessica B Dec 13 '14 at 8:28