I have looked at the cation anion ratio of cubic, octahedral and tetrahedral arrangments on an internet site. By a mathematical derivation they find the minimum value for the cation anion ratios for cubic, octahedral and tetrahedral arrangments. My problem is that even though I get the mathematics I dont get why the derivations show that there is an interval of values that the cation anion ratios for the cubic, octahedral and tetrahedral arrangments can have. I only get that they can have the values that they derive which is(adsbygoogle = window.adsbygoogle || []).push({});

cubic: 0.732

octahedral: 0.414

tetrahedral: 0.225

I need a mathematical justification on why it is an interval of values for the arrangments that in fact are

cubic: 0.732 to 0.999

octahedral: 0.414 to 0.732

tetrahedral: 0.225 to 0.414

I have uploaded a derivation online that says mathematically how the minimum values are found. In addition the question about how the intervals are found are posed there as well The answer is not mathematical. Can anyone help me in finding a mathematical answer to the intervals? The intervals are also in the attachment from an inorganic chemistry book.

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# Problem about lattice structure proof

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