Twisted ammonia model for

One sometimes encounters the statement that a rotational axis which is threefold, C3, or above (C4, C5 etc.) shows cylindrical symmetry. Now, the view down the C3 axis of a molecule such as ammonia shows something more bumpy than cylindrical, so just what does cylindrical symmetry mean It means that, as long as they remain mutually perpendicular, the x and y coordinate axes can be placed anywhere perpendicular to the C3, Q, C, etc. axis (this axis is conventionally chosen as z). Of course, some choice of X, y directions may be more convenient—they lead to simpler mathematics and simpler pictures, but any other choice would be just as acceptable and would in no way change the final result. In a cylinder, x and y can be chosen anywhere perpendicular to the principal rotational axis so, too, here. What applies to x and y coordinate axes also applies to p and Py atomic orbitals, and, for us, this is the important aspect of cylindrical symmetry. 

Return now to the P4 molecule, and regard the contribution to the bonding from each phosphorus to arise from orbitals such as those of Fig. 15.5(b). Because they point towards the centres of faces of the P4 tetrahedron they combine to give three-centred bonding orbitals of the sort shown in 

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