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I think it's common in geology to show the different minerals and soils, and in construction to show how the elements are fastened, but I can't find the right term.

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It is a cross section. Merriam-Webster:

1a : a cutting or piece of something cut off at right angles to an axis also : a representation of such a cutting

...

3 : a composite representation typifying the constituents of a thing in their relations

Here is a cross section of the Earth from USGS. Notice that the section looks as if the Earth were sliced along a vertical axis:

enter image description here

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