What's the name of each pseudo-rectangle in a spherical surface?

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Consider the common surface of a spherical segment crossed with a spherical wedge. This produces a pseudo-rectangle in the sphere surface, and a perfect rectangle in a mercator projection. What's the name of it? Does it have a special name? How do you think we should call it?

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It would not really have a special name, because it does not have straight sides. It is true that the lines of longitude are straight, but the lines of lattitude are curved (ie being parts of circles which are not great circles).

You might try something like 'quadralateral' or 'quadragon'. Rectangle fits too, since all the angles are right-angled (which is what that word means).

The lines of lattitude are often called 'parallels', even though they are more 'equidistants'.

As long as you make the distinction clear, you could call it a rectangle.