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.
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.
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."
