Question

why the crystal structure of water have lower density than that of liquid water ?

Answer 1

We know that Density is the mass of object per unit volume.
$density = \frac{mass}{volume}$
Due to crystal structure of water the volume of water increases due to space between crystals. As density is inversely proportional to volume, the density of water decreases.

So, the crystal structure of water have lower density than that of liquid water.