How can these tiles be considered a model of an ionic solid?

The Black square are considered as the lattice points (Atoms)

= lattice point

Since there is regular arrangement of atoms , therefore it is considered as the ionic solid.

Explanation:

Consider the following points :

Ionic Solids : Those solids which are formed by continuous arrangement of cations(positive charge) and anions(negative charge) bounded by strong force of attraction are called ionic solids.

When These cations and anions  arrange regularly in space, they form Crystal Lattice.

Crystal Lattice : A regular 3-D arrangement if the points in space .

Here the whole figure is Crystal Lattice.

Lattice Points : Each Point in the lattice is called lattice point.

One lattice point represent one Particle , it can be the atom , the molecue or the ions .

In ionic solid these lattice points are ions

= Lattice Points = ions  

These lattice points are joined by a straight line to bring out the Geometry of the Lattice.

So In the given figure  :

 = Ions

The figure as whole = Crystal lattice

And also known as Ionic Solid

Hence these ties can be considered as the model of ionic solids.

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