Most view frustums are 35 to 45 degrees, the angle of each of the four sides as they slope from the near plane to far plane. These are exterior angles. A 36 degree frustum has interior angles of 144 degrees. The projection transform generates a box, rather than a frustum. The sides with 144 degree interior angles swivel in to 90 degrees.
Now consider that a 10-sided prism, a decagon prism, has the same angles as the frustum. If the viewer sees one of its faces orthogonally, as a flat 2D surface, it's neighboring faces will virtually disappear after the projection transform, reduced to 90 degree angles.
Am I correct or wrong?
Wrong (see below for explanation why).
Field of view is usually defined as an internal angle. However this isn't really important to the general point of the question, so let's just ignore it, it just means that the FoV angle is specified one way instead of another.
The hidden assumption here is that what determines the visibility of a face is:
This seems reasonable on the surface, but it's actually wrong. All of these things influence whether a face is visible to a viewer, but they don't actually determine it on their own. What's missing from the equation is the viewer's position.
What actually determines whether a face is visible to a viewer is whether the viewer's eye position lies on the correct side of the plane that the face lies on, extended in all directions to infinity. Secondarily, the face must also be in the viewer's field of view.
To convince yourself of this, stand in front of a door that opens towards you, and open it about 60 degrees. Then take a couple of steps back. You should be able to see the side of the door that faces the room you are standing in. Now walk forward through the door, facing forward the whole time. At a certain point, the side of the door you could originally see will become invisible, and the other side of the door will become visible. Obviously, the angle of the door hasn't changed, and neither has the direction you are facing, so what has caused the change in visibility is not the angles but the fact that you have passed from one side of the plane that the door lies on to the other.
Here's a diagram to illustrate this in the case of a decagon:
The diagram shows a top down view. The red line represents the plane of one of the faces of the decagon. The blue dots represent different viewer positions and the blue lines represent the field of view angles. When the viewer's eye position is on the "Can't see Face A here" side of the plane, Face A will not be visible, and vice versa for the other side.
For a viewer who "sees one of its faces orthogonally, as a flat 2D surface" (the front face), they will be able to see Face A at position 3 (indicated by the green line), but not at position 2 (because of the narrow FoV), and not at position 1 (because of being on the wrong side of the plane that Face A lies on).