The paper defines \((a, d)\)-face antimagic labeling of a certain class of convex polytopes. The possible values of \(d\) are determined as \(d = 2, 4\) or \(6\). For \(d = 2\) and \(4\) we produce \((9n + 3, 2)\) and \((6n + 4, 4)\)-face antimagic labelings for the polytopes.