Context: Conducting Sheets
The problem specifies a box made of thin conducting sheets. While typical cube problems involve wire meshes, the symmetry argument for a sheet-based cube leads to a similar result for the boundaries.

Symmetry Argument:
Imagine a plane that cuts through the cube, perpendicular to the main body diagonal (the line from the input corner to the output corner).

• This “equatorial” plane intersects exactly 6 edges of the cube (the edges that are neither touching the input nor the output directly). Edge BE is one of these edges.
• These 6 edges act as the bridges connecting the “input half” of the cube faces to the “output half.”

Current Distribution:
Due to the perfect symmetry of the cube structure relative to the diagonal axis:

• The total current I must be distributed equally across these 6 boundary connections.
• Therefore, the current crossing the boundary defined by edge BE is:

Current = I / 6