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Regardless, of whether wings are hull or not, I don't think they should be considered when determining the facing. It's pretty clear that they do not constitute the 'corners' of the vehicle, unless your vehicle has six corners on it......

Either that or the front facing is huge (along with the rear), and the sides become even smaller than the rear facing was.

The diagrams look like a corner to corner line. If it is a square shaped vehicle, then its pretty much 45 degree angles, if it is rectangular, then its roughly 30,150,150,30 angles. Oh and I would count the wings in the facing and measurements because they are considered part of the hull.

OH GOD, not the Valkyrie!
The Valkyrie needs an FAQ the size of a small book.
You want to play it by the book, FINE, here is the Valkyrie by the book, all flaws included.
1. Grey Nights take up 1 transport slot each.
2. The wings are not part of the Hull. If a ramming plate, or dreednaught arms aren't part of the hull, neither are wings. Troops can't exit from the edges of the wings either. The hull is the body of the vehicle.
2. b. This does mean that if a Valkyrie sits behind a solid tower wide enough to cover it's hull, but it's weapon mounted wings stick out the side, it can fire those weapons and not receive return fire from that direction (except from drifting ordinance/barrage).
3. It's flight stand is a gorram disaster. Troops can use the special rule to deploy, but they can only mount/deploy normally if the Valkyrie gets friendly with a very tall non impassible terrain feature.
3. b. There are legal ways around this by either modifying the flight stand, or adding a rope and basket to the model.
4. The Valkyrie, like a few other units, may actually be unplayable in certain games if the deployment zone is too small.

Feel free to use house rules as needed.

I loved the vehicle data sheets from Second Edition they were nifty.