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I was looking for a standard name of the set $\{x \in A : x_1 \leq x_2 \leq \cdots \leq x_n\}$, where $A = [0,1]^n$ or $A = [0,\infty)^n$. I think I saw this recently, but now I cannot find it anywhere.

Thanks in advance.

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    In the case $A=[0,1]^n$ this is an $n$-simplex.2012-03-30

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The second one is a Weyl chamber, the first one a Weyl chamber (for the same root system) truncated at level 1.

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    @SetMaster: You are welcome.2012-03-30
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In geometric terms this is an n-simplex called a Schläfli orthoscheme when $A = [0,1]^n$.

The case when $A = [0,\infty)^n$ is an unbounded convex region, but very similar to a simplex in that it is simply a limit of the simplex as coordinates of the first figure are scaled up. One may well refer to this figure as the non-negative cone of the respective $(n-1)$-simplex.

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    @MarianoSuárez-Alvarez: In my rush to improve, I went wrong! New term, new link.2012-03-30
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it is the weyl chamber for the symmetric group

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    Could you provide some more information?2012-04-03