Fractal Imaginary Cubes (i.h.kyoto-u.ac.jp)

I have a 3D-printed Sierpinski Tetrahedron. It's lovely.

https://imgur.com/a/oZwCFLu

This page may be a bit confusing, out of context.

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

This has inspired me to imagine a fractal chandelier design, e.g made of cut glass

Being able to see a shadow and learning that it has area zero made me think that there is something wrong with the definition of area.

Such a cube, i.e., a set, is closed, right? Sooo, there exists a function on the space that is 0 on the cube, strictly positive otherwise, and infinitely differentiable.