Nekar Xenos wrote:

> That is exactly what I was asking. Not for it to be an impossible 
> object, but rather an assertion that the impossible object is not 
> impossible, it is 4d. My question is where can I find a formula to 
> prove/disprove this?

That was not quite what I meant. I was pointing out that the
question is not well-defined because the "impossible" object is
not necessarily any sort of geometric object (not even a mathematical
abstraction in n-dimensional space). It is just a conflict in your
brain because it locally misinterprets the 3d structure of the image
and can't get to a consistent model.

Of course you can define a 4d object that looks like the impossible
object in 2d projection, but so you can in 3d (it's the possible object
Eriban is actually building). Who can say it is or is not the object
that you (fail to) imagine when you encounter the illusion.

Of course, there exist objects in 4d space that have 3 or less
dimensions and still cannot be embedded in 3d space. A famous example
is the Klein Bottle. But I think this is a different matter.

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