Does graphing $ 0 \leq x \leq y \leq z \leq 1 $ and $ 0 \leq x \leq y \leq z \leq \Sigma \leq 1 $ result in a tetrahedron and a pentatope, resp.?

Question

Graph $$ 0 \leq x \leq y \leq 1 $$

Simple.

Now
Graph $$0 \leq x \leq y \leq z \leq 1$$ Would this simply be a tetrahedron with base shown above and the same triangle in the $yz$ and $xz$ planes?

One step further...
Graph
$$ 0 \leq x \leq y \leq z \leq \Sigma \leq 1 $$ Does this produce a $4$-simplex, specifically a pentatope?