\documentclass{amsart}
\usepackage{amsmath,amssymb,nopageno}
\usepackage[all]{xy}
\begin{document}
\begin{align*}
\underset{\text{\large(lower cap)}}{\xymatrix@=2em{
X' \ar[dddd] \ar[ddrr]_i^{[1]} & & & & Z \ar[llll] \\
& & d & & \\
& + & Y \ar[uurr]_v \ar[ddll]_j & + & \\
& & d & & \\
Z' \ar[rrrr]^{[1]} & & & & X \ar[uull]_u \ar[uuuu]_{v \circ u}
}}
&&
\underset{\text{\large(upper cap)}}{\xymatrix@=2em{
X' \ar[dddd]^{[1]} & & & & Z \ar[llll] \ar[ddll] \\
& & + & & \\
& d & Y' \ar[uull]^g \ar[ddrr]_{[1]} & d & \\
& & + & & \\
Z' \ar[uurr]^f \ar[rrrr] & & & & X \ar[uuuu]_{v \circ u}
}}
\end{align*}
\end{document}

DescriptionAxiom TR4 (caps).svg	A depiction of axiom TR4 of a triangulated category. The figure in File:Axiom TR4 (polyhedron).svg is rendered two-dimensionally as its upper and lower halves
Date	14 January 2009
Source	Own work (Original text: I created this work entirely by myself.)
Author	Ryan Reich
Other versions	File:Octahedral diagram variant.svg, File:Axiom TR4 (caps).svg
SVG development InfoField	The SVG code is valid.   This diagram was created with an unknown SVG tool.

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