Penrose Triangle or Tribar"

This two dimensional image suggests a three dimensional object composed by three "bars". Any two consecutive bars are orthogonal in their common end point as can be seen by decomposing the object.

However, by viewing the three bars together, it's easy to observe that this interpretation is wrong and leads to a solid object that isn't closed! Starting from the blue and red bars and following the red and yellow bars, we see that the yellow and blue bars don't join.

The impossible object we started from is an example of a Penrose triangle or tribar.
It occurs in the work of the 20th century swedish artist Oscar Reutersvärd and in "De Waterval", a famous lithograph by M. C. Escher.

To construct a three dimensional object that leads to the original two dimensional image, we start with four mutually orthogonal bars. The right yellow one has been cut off.


The most important part is to determine an orientation of the object in such a way that, when viewing the solid it seems as it has the form of a tribar. To determine this orientation, some rather elementary calculations are needed. Perhaps you can try it yourself. The two yellow bars have to be in a position as if they form just one bar. The reason why one of the yellow bars has been cut off is to obtain a smooth "junction" between the two yellow bars in the raytraced image.


Afterwards, we can rotate the object without any problem around an axis that is perpendicular to the image plane, but rotating it around any other axis gives unwanted effects.


All images have been raytraced using PovRay and the examples on the Porrey 61 site helped me a lot to produce them.

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Herman Serras, December 2004