"Escher" models (was "Modelling Exercise")

Following Heikki's "Modelling Exercise", I made some more "impossible
geometry" models
They're on http://www.dynabits.com/gallery/escher.htm
The "strange hex nut" is very simple to model once you get the idea from
someone else...
The "Penrose Triangle" is IMHO very challenging.
Took me a long time to model something far from perfect...
Can anyone make it simpler and better ?

This gave me an idea for an enhancement request (or an add-in...) : add a
way do draw and constrain sketches in view coordinates, for example to draw
a triangle that looks equilateral in isometric view... "Convert entities" in
view coordinates could also help. Useful ?

 

The "Penrose Triangle" is IMHO very challenging.

Hmm, In my opinion the penrose triangle was very easy to model. By using
lofts it may be difficult, indeed, and you seem to have an extra "edge" in
the model. I will submit my version later, but I need to remodel it since it
seems to be lost. I'd prefer to use straight extrusions instead of lofts;
for example in your version of the "modelling exercise" you can actually see
the curvature of the spokes in the wooden texture.

-h-

 

I will submit my version later, but I need to remodel it since it

And here they are:

http://naakka.dyndns.org/misc/escher_triangle.jpg
http://naakka.dyndns.org/misc/escher_triangle.sldprt

-h-

 

Argh! your solution is so simple ;-)
I started the same but then missed the point with the cut in ISO-plane...
I'll link your solution on my page.

 

it's ok to create the layout sketch on a plane with the desired orientation,
but then you cannot use "Convert Entities" to project them on the "useful"
planes to build the model because "Convert Entities" and other sketch
constraint project entities perpendicularly to the destination sketch (the
one being edited), not to the source sketch as needed here.
Or am I missing something ?

For example if you take Heikki's great Escher triangle and start by
sketching an equilateral triangle on his "ISO-plane", you can't project it
on Face/Top/Right planes and guess that the triangle could be built so
simply...

 

You could actually model the triangle as sheetmetal, and do a flat pattern.
Then you could cut and bend the triangle eg. from paper. This makes it
possible to take a photograph from somebody holding the impossible triangle;
the viewpoint has to be chosen carefully. I have seen such photos somewhere.

-h-