# Does this kind of "partition" have a name?

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")?

• 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 Feb 5, 2023 at 15:03
• There is a dissection tag at math.stackexchange, but the polyhedra are not always restricted to be convex. Feb 5, 2023 at 16:47
• I reposted on math.stackexchange (I hope without breaking any rules)
– pele
Feb 5, 2023 at 16:49
• @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. Feb 5, 2023 at 16:57
• Cross-posted on math.stackexchange. Feb 6, 2023 at 5:41