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Is there an established name for the region between two parallel planes? I can use sheet, layer, lamina... but I'd like to know whether there is an established name for it.

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    $\begingroup$ According to the help center I have to "clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking." I think that the "region between two parallel planes" is not a hard concept to grasp, at least in this forum. And I guess such concept must have a name. What's wrong about asking "Is there an established name for the region between two parallel planes?" Is my English that bad? $\endgroup$
    – aerobiomat
    Commented Oct 15, 2019 at 18:53
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    $\begingroup$ To prevent this question from being closed a second time, you should be more precise about what you mean by parallel planes. Are you looking for terms in synthetic geometry (where points, lines, angles, curves and surfaces are all irreducible primitives)? Or are you looking for terms in analytic geometry (interpreting everything in terms of euclidean space)? $\endgroup$
    – user21820
    Commented Mar 31, 2021 at 14:33
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    $\begingroup$ The question was nicely answered long ago, but your comment piques my curiosity to know the name in each of the cases you mention. $\endgroup$
    – aerobiomat
    Commented Mar 31, 2021 at 17:35
  • $\begingroup$ Well, that's good then. I didn't actually realize your question was an old one but came here because of the close/reopen votes. In any case, thanks for replying! $\endgroup$
    – user21820
    Commented Mar 31, 2021 at 17:39
  • $\begingroup$ I guess I should say that I don't think there is a term for it in synthetic geometry, since usually we phrase things in terms of the points and curves. $\endgroup$
    – user21820
    Commented Mar 31, 2021 at 18:28

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This is called a slab. For example, Boyd and Vandenberghe, Exercise 2.12(a):

A slab [is] a set of the form $\{x \in \mathbb R^n \mid \alpha \le a^T x \le \beta\}$.

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  • $\begingroup$ Thank you for the answer and the link. It seems there are others who don't understand what "a region between two parallel planes" is. $\endgroup$
    – aerobiomat
    Commented Oct 15, 2019 at 18:50
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    $\begingroup$ I don't understand why the question has been closed. I have voted to reopen it. $\endgroup$
    – user856
    Commented Oct 16, 2019 at 4:39

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