> I've been staring at this for 20 minutes and I'm obviously missing 
> something really obvious. Would one of you be kind enough to point out 
> my mistake?

The front left bottom corner (A), 
the rear right bottom corner (B), 
and rear right upper corner (C),
form a right triangle ABC where
length AB = sqrt 2
length BC = 1
length CA = sqrt 3
so the angles are 
BAC = 35.264389
ACB = 54.735610
ABC = 90
so

box {0,1
   rotate 45*y
   rotate 54.73561*z
... etc

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