How do I superimpose two math symbols?

Question

I want to create a symbol that superimpose \top and \bot. I have done this

\documentclass[12pt]{article}
\usepackage{amsmath}
\newcommand{\modd}{\top\hspace{-3.17mm}\bot}
\begin{document}
$\modd \top \bot$
\end{document} 

But the vertical bar seems too thick. I have detexified the symbol and browsed through the comprehensive list, without success.

Answer 1

You guessed a wrong value of the negative space. You needn't guess, TeX can do the work for you.

\documentclass{article}

\makeatletter
\newcommand{\modd}{\mathord{\mathpalette\denis@modd\relax}}
\newcommand{\denis@modd}[2]{\ooalign{$\m@th#1\top$\cr$\m@th#1\bot$\cr}}
\makeatother

\begin{document}

$\modd\top\bot$

\end{document}

See https://tex.stackexchange.com/a/22375/4427 for more information on \ooalign.

Answer 2

\documentclass[12pt]{article}
\usepackage{amsmath,stackengine}
\newcommand{\modd}{\ensurestackMath{\stackengine{0pt}{\top}{\bot}{O}{c}{F}{F}{L}}}
\begin{document}
$\modd \top \bot $
\end{document} 

If you need it at smaller math styles:

\documentclass[12pt]{article}
\usepackage{amsmath,stackengine,scalerel}
\newcommand{\modd}{\ThisStyle{\ensurestackMath{\stackengine{0pt}%
  {\SavedStyle\top}{\SavedStyle\bot}{O}{c}{F}{F}{L}}}}
\begin{document}
$\modd \top \bot $

$\scriptstyle\modd \top \bot $

$\scriptscriptstyle\modd \top \bot $
\end{document}