By ‘imaginary cube’, Hideki Tsuiki means a three-dimensional object that is not a cube, but which nevertheless has square projections in three orthogonal directions, just like a cube does. Examples include the cuboctahedron and the regular tetrahedron.
His previous work on non-fractal imaginary cubes is written up at https://www.mdpi.com/1999-4893/5/2/273
I would assume the problem with the idea is in the fractal physics rather than the definition of area, which has been solidly useful for me.
dmd•3mo ago
https://imgur.com/a/oZwCFLu