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Consider a convex polyhedron $A$. Assume we have subsets $A_1,\ldots,A_n$ of $A$ that are themselves covex polyhedra and are mutually disjoint except maybe sharing an edge, and that their union gives $A$. A simple example would be $A=[0,10]$ with $A_1=[0,3]$, $A_2=[3,6]$ and $A_3=[6,10]$ (observe $A_1$ and $A_2$ are disjoint except for a common extreme point, and so are $A_2$ and $A_3$, and their union gives $A$).

What do we call this sort of partition-like subdivision of $A$ (in addition to a "cover")?

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  • $\begingroup$ It's a pure math problem and should be asked on math.stackexchange. if you just want a name I think it's additionally called decomposition $\endgroup$ Feb 5, 2023 at 15:03
  • $\begingroup$ There is a dissection tag at math.stackexchange, but the polyhedra are not always restricted to be convex. $\endgroup$
    – RobPratt
    Feb 5, 2023 at 16:47
  • $\begingroup$ I reposted on math.stackexchange (I hope without breaking any rules) $\endgroup$
    – pele
    Feb 5, 2023 at 16:49
  • $\begingroup$ @pele of course not. It's just that the other site may have more active experts interested in pure math questions. So ensuring you've posted there as well. $\endgroup$ Feb 5, 2023 at 16:57
  • $\begingroup$ Cross-posted on math.stackexchange. $\endgroup$
    – A.Omidi
    Feb 6, 2023 at 5:41

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What you are describing is often referred to as a "tesselation" or "tiling". I believe they are studied a fair bit by people working on computer graphics.

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