What is the direct product S² × S² × ... × S²?

[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 $S^1$.