(Polar molecules, Non-polar molecules, etc.)
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For all of the other VSEPR models, replacing an atom with a lone pair is done by taking away from the equatorial plane. But with the octahedral shape, an axial bond is replaced to form square pyramidal. Why is that so?
The axes are not relevant for an octahedral shaped molecule because the shape is the same no matter how the molecule is rotated. So any of the planes can have the four atoms with the two lone pairs above and below.
With every other VSEPR shape, 1 removed molecule removed will affect the configuration in different ways with respect to the one removed, thus resulting in different possible bond angles in some. With octahedral, no matter which one is removed, the result will always be the same.