meaning of multi-interval

Question

According to the following definition, a multi-interval is just a line segment for n=1, a square region for n=2, a cubic for n=3, and so on so forth, correct?

Answer 1

Not necessarily a square region ($n=2$) and a cubic region ($n=3$), but rectangle and a box. For higher dimensions the word used seems to be hyperrectangle.

A multi-interval is often written as for example $[a_1, b_1] \times (a_2, b_2) \times \cdots \times (a_n, b_n]$.