Question

I would like to draw an octahedral diagram in my paper; I would prefer to present it as the 'upper hat' + the 'lower hat' (as it is common in the texts on triangulated categories). Could anyone tell me where I can find this diagram (certainly, the 'upper hat part' is sufficient) written down in latex. Maybe, someone could just share with me his own latex realization of this diagram (so that I could replace the original names of objects and morphisms by the ones I need)?

Answer 1

Mikhail,

Here's an upper cap in xy-pic

\xymatrix{ X'\ar[rd]^{[1]}\ar[dd]^{[1]} & & Z\ar[ll] \\ & Y\ar[ru]\ar[ld] & \\ Z'\ar[rr]^{[1]} & & X\ar[lu]\ar[uu] }

at least it's enough of one to get you started. Note that I didn't construct it by hand. I have a script for building these kinds of diagrams visually:

http://www.math.purdue.edu/~dvb/scripts/arraymaker

If it's useful to you, help yourself.

Answer 2

I think that this is an easy exercise in xy-pic. The exact diagram you want may not be in this user's guide, but the basics of xy-pic are easy enough that you should be able to create what you want.

Answer 3

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}

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Changed from an octagon.