How to Calculate the Madelung Constant for an Octahedral Arrangement?

[abstracted6]

Homework Statement

Calculate the Madelung constant for an octahedral arrangement of doubly charged anions about a doubly charged cation. Use r0 for the anion−cation distance. (Hint: Remember that the Madelung constant considers the sum of Coulomb interactions over all atom/ion pairs).

Homework Equations

Possibly helpful Equations
E_A=-(Mke²)/r₀

α=2M/((n₁+n₂)|Z₁Z₂|)

E_A=-(ke²α(n₁+n₂(|Z₁Z₂)/2r₀

The Attempt at a Solution

So we have a theoretical bond pair X⁺²Y^-2 with a coordination number of 6.

I believe the next step should be to calculate E_A, but I fail to see how to do that without α.

 

[Liquidxlax]

Your Madelung equation doesn't seem familiar to me, what textbook are you using?

 

[abstracted6]

Here is a screenshot of my professors notes I took these equations from.

This is our book:

https://www.amazon.com/dp/0521651514/?tag=pfamazon01-20

What equations would you have used?

 

[Borek]

None of these. Madelung constant is calculated just by summing electrostatic interactions between ions.