Here is a schematic of its medial axis. The seams are represented by straight lines.
The sixteen empty magenta squares are planar sheets. They lie within the bisector of the top and bottom of the box.
The pizza box with n spikes in each direction is an example of a polyhedron of Theta(n) complexity having a medial axis of Theta(n2) complexity. More interestingly, it has Theta(n2) medial sheets governed by the same pair of faces. This example was conceived by Jeff Erickson.