A cardboard model of the "impossible" Penrose triangle.
Gerard Westendorp
Other stuff by me

This page is to explain how to make a cardboard model of  the "impossible" Penrose triangle.
This is a 2 dimensional picture, that locally looks like it could exist as a 3 dimensional object, but as a whole, it seems impossible.
Below is a picture in isometric projection.

Isometric projection of Penrose impossible triangle

The three cube shaped vertices of the triangle appear to be at the midpoints of the edges of a larger cube.
At each of these vertices, the bars looks as if they are orthogonal, and as if they extend in a straight line to another vertex.
This is not possible in 3D. Also, you can't have an equilateral triangle with 3 angles of 90 degrees.

The trick is that the world is 3D but a picture is 2D. So you lose 1 dimension. Normally our brains reconstruct a 3D object anyway. But here we have an object that is specially designed to trick you when viewed from a specific angle.

Penrose impossible triangle Penrose impossible triangle

Usually, the Penrose triangle is done by making 2 copies of 1 of the 3 bars, that are exactly behind each other, which stop in mid space, never reaching the other corner. Which is not visible to the viewer.
Recently I saw a Tweet in which the trick was done by using bent bars. The bending direction is exactly in the projection direction, so it can be made invisible to the viewer. I thought it was pretty cool, so I decided to make a cardboard model of it.

According to Wikipedia, "This type of Impossible Triangle was first created in 1969 by the Soviet kinetic artist Vyacheslav Koleichuk."

Here is a Youtube clip:

Here is the cut-out: (Click and download)
Cut-Out for cardboard penrose triangle

I was inspired to make this web site by this Tweet from Tomoya TENDO:


— Tomoya TENDO (@end_tt) January 7, 2021