Why is ice less dense than liquid water?

I understand that the difference between the structures of ice and liquid water is that every H atom in a H2O molecule is hydrogenly bonded to a O atom on another H2O molecule in ice, whereas in liduid water not every H atom is hydrogenly bonded to a O atom on another H2O molecule.
That makes ice have a structure like diamond, whereas liquid havn't.
I can see that there are spaces (gaps) in the structure.
Are the spaces exsist in ice the reason that ice is less dense than liquid water?