If you can make a precise miter, it does this fine. The trick is in making it precise enough, and gluing it without allowing it to slip.
There is a family of standard joints, either originated by or made famous by the Stickley company (who were trying to get quarter-sawn faces on all 4 sides of an oak leg), that help with the slipping-when-gluing aspect by adding a key to the surface.
A picture would be delightful here but I'm uncomfortable with the rights status (for me to post it here) of anything I can find, so go have a look around the web with that in mind.
I have also seen this done by making a VERY precise V-groove that does not QUITE go through the face veneer at each joint location, and then gluing and folding - the face veneer is continuous on 3 corners, which helps hold it from slipping and also looks "seamless." You'll have to judge whether this is within your tools and skills or not.