Impossible objects: The Penrose Triangle

The Penrose triangle is one of these shapes that seems impossible to build but that you can model for fun and then print. Theres are aready a few version on thingiverse but they are with an open loop (here or there). I will here go over a short tutorial with Autodesk Inventor to build one version of the said triangle with a closed loop.

  1. On a new part file we will first draw the “L” outline of the triangle with 2 square on each end with diagonal as construction lines. I try to keep most of the distance parametric so i can update the object faster after (in this case length=40mm, & side=5mm). Then extrude the whole profile by side amount
    penrose_step1
  2. On the bottom side of the L, create a sketch then project one of the center point that will be used for the next construction step and as a profile of the final loft.
    penrose_step2
  3. Create a three points plan using 2 opposite corners of one square of the first sketch and the center point from the sketch under the L shape.
    penrose_step3
  4. To build the sweep of the third side for the Penrose triangle, we need a profile. Add a sketch on the plane we just created. Project the 2 square center points and draw a construction line in between. Then add a three points spline that goes from one center to the middle point to the next center point. Activate the handle of one of the end points and add a vertical constraint on the handle. The spline should make a nice symmetric curve.
    penrose_step4
  5. Exit the sketch, and build a sweep using the top square as the profile and the spline as the path.
    penrose_step5
  6. Enjoy your new Penrose triangle. You may want to experiment with the length and the side to get a good looking result. Try to minimize the curve of the spline without creating a self intersecting profile.
    penrose_final

The STL file is available on Thingiverse here, the Inventor part file is here.

Edit 4/19, I’ve finally printed this object, see here!

penrose_final

penrose_final_side

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