Impossible objects explained

I occasionally draw something like this on the board and ask my students what it is:

When they reply 'a cube' I correct them, saying that it is a two dimensional drawing that uses tricks of perspective that our mind interprets as a three dimensional cube. Two dimensional drawings of impossible objects take advantage of these tricks of perspective, but the tricks don't match up. So if you cover up one part of the drawing and then cover up the other part of the drawing, different sections appear to be going in different directions. For example, take the famous devil's fork:

If you cover up the right-hand portion, you see three prongs, but if you cover the left portion you see two prongs. However, the lines connect up so at some point the three become two, or the foreground becomes the background. But how to achieve this in three dimensions? The whole idea of an impossible object is that it is impossible. The answer, of course, is that you can only see these from one particular point of view. If you were to look at them from any other angle, you would see that the edges don't match up. For instance ...

Brixe63's Terrace.



Legohaulic's Nightmare.



Henry Lim's Ascending and Descending.



Andrew Lipson and Daniel Shiu's Belvedere.

Impossible objects

Several of the Escher illustrations depicted over the past few days are impossible objects - two dimensional drawings that seem to be of three dimensional objects, but turn out to be optical illusions, unbuild-able in real life. One of the first impossible objects, and one of the inspirations for Escher's Waterfall and other works, is known as the Penrose triangle. This was actually first depicted by Oscar Reutersvärd in 1934, before Roger Penrose independently presented his version.

The Penrose Triangle was the basis for the Lugnet logo. Lugnet was one of the first major LEGO websites.

John Langrish made this mosaic of the Lugnet Logo.

The Penrose Triangle has been recreated in LEGO many times. Some of these depend on Photoshop trickery, but others are true three-dimensional creaions, such as this by Billy Baldwin.

Brixe63's Modulex version is more remniscent of Reutersvärd's original design.

Various other LEGO impossible objects have been built, such as Don Solo's archway.

Brixe63 has had great fun with the idea in her set of optical illusions.



Brixe63 also has this amazing Terrace, that is based on an impossible scene that was apparently first used by Sandro del Prete (who was influenced by Escher).

More Escher roundup

Other Escher works have also been recreated in LEGO form, including ...

Day and Night by BrickWares.


Balcony by Andrew Lipson and Daniel Shiu


Drowned Cathedral by Minkowsky


Sky and Water I seen at Legoland


Reptiles by Profound Whatever


Double Planetoid at the Billund airport


Three Spheres II by Gwaehur


Rose by Aaron K


Drawing Hands by Ian Leino


... and by Littlehorn


... and by B.K.


... and by j p

Escher: Waterfall

A few takes on Escher's 'Waterfall':

Andrew Lipson and Daniel Shiu.

Henry Lim.

Jung von Matt advertising agency.

Legohaulic's Nightmare drew inspiration from Waterfall.

Escher: Belvedere

Belvedere has been another subject for LEGO Escher fans.

Andrew Lipson and Daniel Shiu.

Henry Lim.

Jung von Matt ad agency.

Brixe63, who has done a number of optical illusions, made some Belvedere-inspired bunk beds.

Escher: Ascending and Descending

Continuing with our look at M.C. Escher in LEGO form, another very popular work is Ascending and Descending:

Probably the earliest version was by Andrew Lipson and Daniel Shiu.

Henry Lim's version.

The advertising agency Jung von Matt made a "create the impossible" ad.

Puriri deVry.

Buge Fun.

Raphael Heusser.

Escher: Relativity

M.C. Escher is surely the most popular artist among mathematicians and scientists. His explorations of symmetry and tricks of perspective and perception and his playful use of geometry all explore themes that are important across all of these fields. Several LEGO builders have taken on Escher themes. The first prominent effort was by Andrew Lipson and Daniel Shiu, who recreated five different Escher works in the early 2000's. In 2005, Henry Lim was commissioned by the Hong Kong Science Museum to make his own takes on four Escher pictures. Others have explored this work in LEGO form as well.

Perhaps the most popular Escher work in LEGO form is Relativity. Here is a version by Andrew Lipson and Daniel Shiu.

And another by Henry Lim.

Paul Vermeesh just recently posted a Star Wars version (which is what prompted this post).

Profound Whatever did a space version.

NewRight did a castle version.

Here's a version by Supernerd23

Big Daddy Nelson built this vignette

Thanks to Nannan of the Brothers-Brick for tracking down a couple of those links.