Is real image always inverted and virtual image always erect with respect to the object? Is there any single optical device (a mirror, or a lens, or anything else) which could produce a real and erect image or a virtual and inverted image? Till now, I haven't encountered such a device. Does it mean this is not possible? Is there any fundamental law which prevents the existence of an optical device which could produce a real and erect image or a virtual and inverted image?
I know that we could produce a real and erect image by using two convex lenses by placing them one after the other, where the inverted image formed by the first lens acts as an object for the second lens which again inverts it to give a resultant erect image with respect to the original object. Here we get an erect image due to two inversions. This question is about a single device which could produce a real and erect image without any intermediate inversion steps.
It was asked in the comments what is meant by a "single optical device". By this term, I meant that the device is made of a single piece of material of same refractive index throughout. So a combination of lenses or mirrors which may produce real and erect images do not count.