We say that a cubical 2-knot \(K^{2}\) is an embedding of the 2-sphere in the 2-skeleton of the canonical cubulation of \(\mathbb {R}^4\) ; in particular, \(K^{2}\) is the union of \(m(K^{2})\) unit squares, and hence, \(m(K^{2})\) is its area. We define the minimal area of \(K^{2}\) as the minimum over all the areas of cubical 2-knots isotopic to the given knot type. The minimal area of a cubical 2-knot is an invariant, and the following natural question arose: Given a knot type, what area is needed for a cubical 2-knot in the canonical cubulation of \(\mathbb {R}^4\) to realise that type with minimal area? In this paper, we answer this question for the spun trefoil knot in the weakly minimal case.
