# Name for this product space

1. Aug 5, 2009

### Tac-Tics

The unit interval is [0, 1].

Is there a name for the cartesian product of n unit intervals? So, [0, 1] x [0, 1] is the unit square, [0, 1] x [0, 1] x [0, 1] is the unit cute. What would you call [0, 1] x ... x [0, 1] with n factors?

I'm guessing there is such a term, because it's a pretty useful geometric object. It's at least as important as an n-torus, which is $$S^1 \times \cdots \times S^1$$

2. Aug 5, 2009

### Newtime

symmetric k-cell?

n-dimensional symmetric k-cell?

I guess you could call it anything so long as there is at least somewhat of a use for it. How about "yourlastname"-Space?

3. Aug 5, 2009

### Tac-Tics

Sweet!

If I were to write a paper on it, I'd probably call it an orthogonal unit. Orthogonal is just a cool sounding word.

But I'd still like to hear if there's a name in common use!

4. Aug 5, 2009

### Dragonfall

It's the geometric unit n-hypercube, or just unit n-cube for short.

Last edited: Aug 5, 2009