%%% barbara beeton: New symbols from old (LaTeX)
% Sometimes one needs a symbol that can't be found in any font,
% but that is either a rotation or a reflection of a sybol that
% is available.  'graphicx' package to the rescue!

\newcommand{\reflectit}[1]{\reflectbox{\ensuremath#1}}
\newcommand{\turnover}[1]{\rotatebox[origin=c]{180}{\ensuremath#1}}
\newcommand{\turnne}[1]{\rotatebox[origin=c]{45}{\ensuremath#1}}
\newcommand{\turnnw}[1]{\rotatebox[origin=c]{135}{\ensuremath#1}}
\newcommand{\turnsw}[1]{\rotatebox[origin=c]{225}{\ensuremath#1}}
\newcommand{\turnse}[1]{\rotatebox[origin=c]{315}{\ensuremath#1}}
\newcommand{\reflectit}[1]{\reflectbox{\ensuremath#1}}
\newcommand{\turnover}[1]{\rotatebox[origin=c]{180}{\ensuremath#1}}

\newcommand{\reflectit}[1]{\reflectbox{\ensuremath#1}}
\newcommand{\turnover}[1]{\rotatebox[origin=c]{180}{\ensuremath#1}}
\newcommand{\turnne}[1]{\rotatebox[origin=c]{45}{\ensuremath#1}}
\newcommand{\turnnw}[1]{\rotatebox[origin=c]{135}{\ensuremath#1}}
\newcommand{\turnsw}[1]{\rotatebox[origin=c]{225}{\ensuremath#1}}
\newcommand{\turnse}[1]{\rotatebox[origin=c]{315}{\ensuremath#1}}
%\newcommand{\reflectit}[1]{\reflectbox{\ensuremath#1}}
%\newcommand{\turnover}[1]{\rotatebox[origin=c]{180}{\ensuremath#1}}

\[
{}\leqslant\;\geqslant{}:\;
  \turnover{\geqslant}\;\turnover{\leqslant};
\qquad
{}\Rightarrow{}:\;
  \turnne{\Rightarrow}\;\turnnw{\Rightarrow}\;
  \turnsw{\Rightarrow}\;\turnse{\Rightarrow};
\qquad
{}\sim{}:\;
  \reflectit{\sim}
\]
