Applying “Escher” like perspective

Hi, I’m a neophyte when it comes to design / 3D work… but really enjoy the challenge of learning something new.

This has got me stumped, though…

I’ve redrawn as a basic 3D object that represents a corporate logo. Very basic - just tracing a logo that was designed for us.
As a part of that project, the designer created an “Escher - like” representation of the mark - handrawn / shaded.

The question is how to realize this in Shapr?

Here’s a link to the SHAPR file

Here’s a link to the hand-drawn Escher-like version

So, ideally, the 3D implementation of this logo has the smallest, inner most “loop” extruded down / behind all the others.
And the largest, outer-most loop is extruded up / in front of the others
and obviously, the one in the middle stays in the middle…

But then trying to “connect” the smaller loop to the larger loop in that Escher like fashion.

Now… I’m fully prepared to resign myself to the potential reality that “Escher-like” can’t be realized in the real world in this way and thats what makes Escher-like anything like Escher! (If that makes sense)

But if that’s not the case and it can be realized, I’d be so very grateful for suggestions on how to accomplish it.

Thanks in advance for your thoughts and suggestions.

As Escher is based on “optical illusion”, there’s no way to really create these shapes in 3D.

But you can apply visual tricks to create “the illusion”. Check out this video for example:

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