Mathematically

if you look at the Front Ortho of the image there is the triangle ABC. Length B is the side of the cube L, length A is the length of a faces diagonal L * sqrt(2) (basic pythagorus)   The tangent of angle alpha will be L / (L * sqrt(2))  or 1 / sqrt(2) atan of which equates to 35.2644 degrees. 

The rotation_euler XYZ (45, 35.264, 0)   

The length of the longest diagonal C is L * sqrt(3), Once again from pythagorus.  If the origin is in the middle of the cube translate the cube L * sqrt(3) / 2 to put it on its point.

Interestingly the volume can be calculated from 

The length of the 
[![enter image description here][1]][1]


  [1]: https://i.sstatic.net/UHdAK.png