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The same example given in xy-pic done in Tikz: More examples and code are at http://www.texample.net/tikz/examples/ and the manual http://mirror.ctan.org/graphics/pgf/base/doc/generic/pgf/pgfmanual.pdf

\documentclass[a4paper]{article}
\usepackage{tikz}
\usetikzlibrary{shapes}
\begin{document}
\begin{tikzpicture}[shorten <=7pt,shorten >=7pt]
    \node [name=oct,regular polygon,regular polygon sides=4,minimum size= 12em] {};
    \node at (oct.corner 1) [name=octCorner1] {$Z$};
    \node at (oct.corner 2) [name=octCorner2] {$X'$};
    \node at (oct.corner 3) [name=octCorner3] {$Z'$};
    \node at (oct.corner 4) [name=octCorner4] {$X$};
    \node at (oct.center) [name=octCenter] {$Y$};
    \draw [-stealth] (oct.corner 2) -- node [right] {$[1]$} (oct.corner 3);
    \draw [-stealth] (oct.corner 1) --                      (oct.corner 2);
    \draw [-stealth] (oct.corner 1) --                      (oct.corner 4);
    \draw [-stealth] (oct.corner 3) -- node [above] {$[1]$} (oct.corner 4);
    \draw [-stealth] (oct.corner 2) -- node [right] {$[1]$} (oct.center);
    \draw [-stealth] (oct.corner 4) --                      (oct.center);
    \draw [-stealth] (oct.center)   --                      (oct.corner 3);
    \draw [-stealth] (oct.center)   --                      (oct.corner 1);
\end{tikzpicture}
\end{document}

Changed from an octagon.