optics - Mirror vs Lens: do either or both invert the image?

Answers to this other Question on photo stackexchange have prompted me to seek clarification on this.

consider for example the following images:

Original scene

How a mirror "sees" it (flipped horizontally hence inverted)

How a lens "sees" it (flipped horizontally and vertically hence NOT inverted)

The mirror image is flipped once, hence it is inverted, but the lens image is flipped twice (horizontally and vertically) hence it is not inverted.

This is all relevant when trying to understand the path of the image through an SLR camera. Using an image from one of the answers to the aforementioned question we have this:

Now, if you use my interpretations to understand the inversions, then you have an odd number of inversions in total. So how then is the image at the viewfinder not inverted? Certainly, something I said is not right. I will leave it to you good people to identify my error and correct it for me.

Answer

The answer is that the pentaprism is actually a roof pentaprism. The image is laterally-inverted (left-right inverted) because the image actually bounces an additional time due to the roof of the pentaprism.

^{Pentaprism diagram from Wikipedia: Single-lens reflex camera, CC-BY-3.0}