From The Baptized Body by Peter J. Leithart:
1 Corinthians 12:12 is particularly striking the way Paul identifies the Head-and- members body of Christ as “Christ.” “‘Christ” is not just the title of the Anointed Head. The anointing flows like the dew of Hermon down from our priestly Head, down the beard, down to the skirts of the garments [i.e. to the individual]. Whoever is touched by that anointing in the Spirit (vv. 12-13) becomes a member of the body of the Head. Whoever is touched by that anointing is part of “Christ.” Together, Anointed Head and anointed body make a single Anointed One, one Christ. Augustine’s idea of’ totus Christus – a “whole Christ” made of Head and body is not a fanciful fabrication of a Plotinian mind. It is purely Pauline. And this “whole Christ” is the visible, historical church. – p. 62