How to produce a 3D-like commutative diagram using xymatrix?

Question

Could somebody give an idea how to create the following 3D commutative diagram?

Welcome! Please post the code you've got so far. Right now, this is just another do-it-for-me. You may get lucky. Or you may not. If you can make your diagrammatic needs cuter and more visually appealing (e.g. include a small dragon or a large duck), you may stand a better chance. However, you may also get only the dragons and ducks, so this might be a problem if they are not the main focus of your work. I recommend specialising in dragon-duck interactions for maximum do-it-for-me yields. Otherwise, a Minimum Working Example is the way to go. Why do you need xy-pic especially? — cfr, Jul 27 '16 at 03:15
Any other solution as convenient as the xy-pic one is welcome! — PhysicsMath, Jul 27 '16 at 03:54

score 5 · Accepted Answer · edited Apr 13 '17 at 12:34

A tikz based solution:

\documentclass{article}
\usepackage{amsfonts}
\usepackage{tikz}
\usetikzlibrary{matrix}
\begin{document}
\begin{tikzpicture}
  \matrix (m) [matrix of math nodes,row sep=2em,column sep=4em]{
     & S(n) & S(n) & \cdots\\
TM   &      &      &       \\
     &      \mathfrak{X}(n, n+q) & \mathfrak{X}(n, n+q+1) & \cdots\\
M    &      &      &       \\};
\path[-stealth]
(m-2-1) edge (m-1-2);  
\path[-stealth]
(m-1-2) edge (m-1-3);
\path[-stealth]
(m-1-3) edge (m-1-4);
\path[-stealth]
(m-4-1) edge (m-3-2);  
\path[-stealth]
(m-3-2) edge (m-3-3);
\path[-stealth]
(m-3-3) edge (m-3-4);
\path[-stealth]
(m-2-1) edge (m-4-1);
\path[-stealth]
(m-1-2) edge (m-3-2);
\path[-stealth]
(m-1-3) edge (m-3-3);
\end{tikzpicture}
\end{document}

Output:

You can simplify this even using one \path. See an example here.

[EDITED by Steven B. Segletes to add \slantbox feature from Shear transform a "box"

For 3-D effect, one can use Bruno's \slantbox. Note in this case, for the isometric effect, the optional argument to \slantbox is the tangent of the rotation angle.

\documentclass{article}
\usepackage{amsfonts}
\usepackage{tikz}
\usetikzlibrary{matrix}
\newsavebox\foobox
\newcommand{\slantbox}[2][.2]{\mbox{%
        \sbox{\foobox}{#2}%
        \hskip\wd\foobox
        \pdfsave
        \pdfsetmatrix{1 0 #1 1}%
        \llap{\usebox{\foobox}}%
        \pdfrestore
}}
\begin{document}
\begin{tikzpicture}
  \matrix (m) [matrix of math nodes,row sep=2em,column sep=4em]{
     & S(n) & S(n) & \cdots\\
\rotatebox{25}{\slantbox[.466]{TM}}   &      &      &       \\
     &      \mathfrak{X}(n, n+q) & \mathfrak{X}(n, n+q+1) & \cdots\\
\rotatebox{25}{\slantbox[.466]{M}}    &      &      &       \\};
\path[-stealth]
(m-2-1) edge (m-1-2);  
\path[-stealth]
(m-1-2) edge (m-1-3);
\path[-stealth]
(m-1-3) edge (m-1-4);
\path[-stealth]
(m-4-1) edge (m-3-2);  
\path[-stealth]
(m-3-2) edge (m-3-3);
\path[-stealth]
(m-3-3) edge (m-3-4);
\path[-stealth]
(m-2-1) edge (m-4-1);
\path[-stealth]
(m-1-2) edge (m-3-2);
\path[-stealth]
(m-1-3) edge (m-3-3);
\end{tikzpicture}
\end{document}

I hope you don't mind that I added a 3-D supplement to your answer. If you don't like it, you or I can roll it back to your prior posting. — Steven B. Segletes, Jul 27 '16 at 10:30
OMG, there is even 3D effect! That is more than what I am looking for! Many thanks for your answer and I am so impressed by your TeX skills! — PhysicsMath, Jul 28 '16 at 02:19

score 3 · Answer 2 · answered Jul 27 '16 at 07:38

The trick is to use four rows, reducing the spacing between rows.

Take your pick among Xy-pic and tikz-cd:

\documentclass{article}

\usepackage[all,cmtip]{xy}

\usepackage{tikz-cd}

\begin{document}

This is the diagram using Xy-pic
\[
\xymatrix@R-.8pc{
  & S(n) \ar[rr] \ar[dd] && S(n) \ar[rr] \ar[dd] && \cdots \\
T(M) \ar[ur] \ar[dd] \\
  & \mathcal{X}(n,n+q) \ar[rr] && \mathcal{X}(n,n+q+1) \ar[rr] && \cdots \\
M \ar[ur]
}
\]

This is the diagram using tikz-cd
\[
\begin{tikzcd}[row sep=4ex]
  & S(n) \arrow[rr] \arrow[dd] && S(n) \arrow[rr] \arrow[dd] && \cdots \\
T(M) \arrow[ur] \arrow[dd] \\
  & \mathcal{X}(n,n+q) \arrow[rr] && \mathcal{X}(n,n+q+1) \arrow[rr] && \cdots \\
M \arrow[ur]
\end{tikzcd}
\]

\end{document}

Looks great even though it is not really 3D diagram. But the trick greatly reduces the amount of coding! Many thanks! And I also appreciate very much the comparison! — PhysicsMath, Jul 28 '16 at 02:21

How to produce a 3D-like commutative diagram using xymatrix?

2 Answers2