S^2 × S^2...×S^2×S^2 is a Direct Product of S^2 - Hypertorus

[LagrangeEuler]

http://en.wikipedia.org/wiki/Torus

$S^1 \times S^1... \times S^1 \times S^1$
is hypertorus.
And what is
$S^2 \times S^2... \times S^2 \times S^2$?

 

[Ben Niehoff]

It doesn't have a name.

Also, nobody says "hypertorus". Typically one uses $T^n$ to mean the direct product of $n$ copies of $S^1$.