Spaces in crystal lattices?

I read that the angle between crystal faces is controlled by the spacing between lattice spaces. What I don't understand is how can there be spaces in crystal lattice if all the atoms are packed together? In other words when you look at any mineral specimen of course you don't see any spaces.

Answer:
Imagine that the atoms in a crystal are like spheres or balls. Even when you pack them as closely together as possible, with nearest neighbors touching each other, there are still some gaps. If you're having trouble visualizing this, as a thought experiment get 9 pennies and arrange them in a 3x3 grid so that the edges of the pennies touch each other. Even though you've packed the pennies together as closely as possible in two dimensions, there are gaps since the pennies are round.

Why don't we see the gaps? Because we're not going to see these tiny, smaller than atom-sized gaps with our naked eyes.

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