Pope Francis has employed the image of an "inverted pyramid" to illustrate his vision of a synodal Church, particularly the hierarchical ministry's exercise of authority. While the reversal of the pyramid succeeds in situating the hierarchy in the people of God, the lens of service in this inverted pyramid falls short in articulating the mutual reciprocity of all baptized faithful that undergirds their common responsibility for the Church's mission, particularly in church governance. I argue that instead, the metaphor of a "polyhedron," alluding from Francis' mediation between principles of universality/particularity and unity/diversity, more adequately represents and makes actionable the synodal vision. The aim of this paper is two-fold: firstly, it examines these two contrasting images and explores their particular expressions and mode of operation. Secondly, it utilizes participation as a hermeneutical lens to expound on the polyhedric directions of authority.