# Big vertices on my cube kill parallelism

I have coded the following diagram in xypic:

\xymatrix{
& B \ar[rr] \ar'[d][dd]^(.45)\simeq && B\cup_A C \ar@{.>}[dd]^-\simeq \\
A \ar@{>->}[ru] \ar[rr] \ar[dd]_-\simeq && C \ar@{>->}[ru] \ar[dd]^(.68)\simeq & \\
& B' \ar'[r][rr] && B'\cup_{A'}C' \\ A' \ar@{>->}[ru] \ar[rr] && C' \ar@{>->}[ru] &
}


It renders like this:

If you are subconsciously symmetry-obsessed like many human beings are (including myself), you will have noticed that the diagonal arrows which are supposed to be parallel, aren't really. This is a side effect of having vertices with different lengths.

Is there an automatic fix to this, some command that prioritizes parallelism over placing the arrows tip/end most centered on the objects? If not, how can I fix this manually for this particular diagram?

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As I don't use xypic, I can't turn this into an answer - besides you already have a good one. It strikes me though that you'd be better off considering the text as labels relating to vertices rather than as vertices - look at how the primes on A' and C' collide with the tails on the arrows - and setting then "outside" the vertices. –  Chris H Apr 3 at 8:53
@ChrisH: thanks for the suggestion. The problem of the primes overlapping with the arrows is solved by passing the cmtip command to xypic. I just rendered the diagram for posting it here in presheaf.com, which apparently doesn't use cmtip. –  Bruno Stonek Apr 3 at 9:06

With help of calc package, make a box of width B with left alignment and put B\cup_A C inside. Do the same for B'\cup_{A'}C'. Here these two quantities protrude to the right, but I hope that is OK.
\documentclass{article}
$\xymatrix{ & B \ar[rr] \ar'[d][dd]^(.45)\simeq && \makebox[\widthof{B}][l]{B\cup_A C} \ar@{.>}[dd]^-\simeq \\ A \ar@{>->}[ru] \ar[rr] \ar[dd]_-\simeq && C \ar@{>->}[ru] \ar[dd]^(.68)\simeq & \\ & B' \ar'[r][rr] && \makebox[\widthof{B}][l]{B'\cup_{A'}C'} \\ A' \ar@{>->}[ru] \ar[rr] && C' \ar@{>->}[ru] & }$