At first glance, it seems that impossible figures can only exist on a plane. In fact, incredible figures can be embodied in three-dimensional space, but for "the same effect" you need to look at them from a certain point.
Distorted perspective is a frequent occurrence in ancient painting. Somewhere this was due to the inability of artists to build an image, somewhere - a sign of indifference to realism, which was preferred to symbolism. The material world was partly rehabilitated in the Renaissance. The Renaissance masters began to explore perspective and discovered games with space.
One of the images of an impossible figure dates back to the 16th century - in the painting by Pieter Brueghel the Elder “Forty on the gallows”, the same gallows looks suspicious.
Great fame came to the impossible figures of the twentieth century. The Swedish artist Oskar Rutesvärd painted a triangle composed of cubes in 1934 "Opus 1", and a few years later - "Opus 2B", in which the number of cubes decreased. The artist himself notes that the most valuable thing in the development of figures, which he undertook back in his school years, should be considered not the creation of the drawings themselves, but the ability to understand that what is drawn is paradoxical and contrary to the laws of Euclidean geometry.
My first impossible figure appeared by chance, when in 1934, in my last class at the gymnasium, I “scratched” in a Latin grammar textbook, drawing geometric figures in it.
Oscar Rutesward "Impossible Figures"
In the 50s of the twentieth century, an article was published by the British mathematician Roger Penrose, devoted to the peculiarities of the perception of spatial forms depicted on a plane. The article was published in the British Journal of Psychology, which says a lot about the nature of impossible figures. The main thing in them is not even paradoxical geometry, but how our mind perceives such phenomena. As a rule, it takes a few seconds to understand what exactly is “wrong” with the figure.
Thanks to Roger Penrose, these figures were looked at from the point of view of science, as objects with special topological characteristics. The Australian sculpture, which was discussed above, is just the impossible Penrose triangle, in which all the components are real, but the picture does not add up to the integrity that can exist in the three-dimensional world. The Penrose triangle is misleading with a false perspective.
The mysterious figures have become a source of inspiration for both physicists and mathematicians and artists. Inspired by Penrose's article, the graphic artist Maurits Escher created several lithographs that made him famous as an illusionist, and subsequently continued to experiment with spatial distortions on the plane.
Impossible fork
The impossible trident, blivet, or even, as it is also called, the "devil's fork", is a figure with three round prongs at one end and rectangular ones at the other. It turns out that the object is quite normal in the right and left parts, but in the complex it turns out to be uniform madness.
This effect is achieved due to the fact that it is difficult to unequivocally say where the foreground is and where the background is.
Irrational cube
The impossible cube (also known as Escher's cube) appeared on Maurits Escher's Belvedere lithograph. It seems that the very existence of this cube violates all the basic geometric laws. The answer, as always with impossible figures, is quite simple: the human eye tends to perceive two-dimensional images as three-dimensional objects.
Meanwhile, in three dimensions, an impossible cube would look like this, and from a certain point would appear the same as the picture above.
Impossible figures are of great interest to psychologists, cognitive scientists and evolutionary biologists, helping to learn more about our vision and spatial reasoning. Today, computer technologies, virtual reality and projections expand the possibilities, so that contradictory objects can be looked at with new interest.
In addition to the classic examples that we have given, there are many other options for impossible figures, and artists and mathematicians come up with new paradoxical options. Sculptors and architects use solutions that may seem incredible, although their appearance depends on the direction of the viewer's gaze (as Escher promised - relativity!).
You don't have to be a professional architect to try your hand at creating volumetric impossibilities. There are origami of impossible figures - this can be repeated at home by downloading the blank.
Useful Resources
- Impossible World - a resource in Russian and English with famous paintings, hundreds of examples of impossible figures and programs for creating the incredible on your own.
- M.C. Escher - official site of M.K. Escher founded by the MC Escher Company (English and Dutch).
- - works of the artist, articles, biography (Russian language).
By entering such a question into the search engine, we will get the answer: “An impossible figure is one of the types of optical illusions, a figure that at first glance seems to be a projection of an ordinary three-dimensional object, upon closer examination of which contradictory connections of the elements of the figure become visible. An illusion is created of the impossibility of the existence of such a figure in three-dimensional space. (Wikipedia)"
I think that such an answer will not be enough for us to present and understand this concept, so let's try to study this issue better. And let's start with history.
Story
In ancient painting, you can find such a frequent phenomenon as a distorted perspective. It was she who created the illusion of the impossibility of the existence of the object. In the painting by Pieter Brueghel the Elder "Forty on the Gallows", such a figure is the gallows itself. But at that time, the creation of such "fables" was not a flight of fancy, but rather an inability to build a correct perspective.
Great interest in impossible figures woke up in the twentieth century.
The Swedish artist Oskar Rutesvärd, fascinated by the creation of something paradoxical and contrary to the laws of Euclidean geometry, created such works: the triangle made of cubes "Opus 1", and later "Opus 2B". 
In the 50s of the twentieth century, an article was published by the British mathematician Roger Penrose, devoted to the peculiarities of the perception of spatial forms depicted on a plane. The article interested a wide range of people: psychologists began to study how our mind perceives such phenomena, scientists looked at these impossible figures as objects with special topological characteristics. Impossible art or impossibilism appeared - a direction in art, which is based on the creation of optical illusions and impossible figures.
Penrose's article inspired Maurits Escher to create several lithographs that brought him fame as an illusionist artist. One of his most famous works is Relativity. Escher depicted the Penrose model of the "infinite staircase". 
Roger Penrose and his father, Lionel Penrose, invented a staircase that makes a 90-degree turn and closes. Therefore, a person, if he wanted to climb it, could not rise higher. The figure below shows that the dog and the person are on the same level, which also adds to the picture of impossibility. If the characters go clockwise, they will constantly go down, and if they go counterclockwise, they will go up. 
It is impossible not to note the impossible Escher cube, which seems impossible, because it is common for the human eye to perceive two-dimensional images as three-dimensional objects (you can read more about Escher). 
And also a classic example of an impossible figure - the Trident. It is a figure with three round teeth at one end and rectangular ones at the other. This effect is achieved due to the fact that it is difficult to unequivocally say where the foreground is and where the background is. 
Currently, the process of creating impossible figures continues. Below are some of them (the name of the creator is under the figure).
And also it is impossible not to note the beautiful impossible figures created by our fellow countryman, Omsk Anatoly Konenko. For example: 
Is it possible to see "impossible figures" in real life?
Many will say that impossible figures are really unrealistic and cannot be recreated. Others will argue that the drawing depicted on a sheet of paper is a projection of a three-dimensional figure onto a plane. Therefore, any figure drawn on a piece of paper must exist in three-dimensional space. So who is right?
The second will be closer to the correct answer. Indeed, it is possible to see “such” figures in reality, it is only necessary to look at them from a certain point. With the help of the pictures below, you can verify this.
Jerry Andrus and his impossible cube: 
The impossible clutch of gears, also embodied in reality by Jerry Andrus. 
Sculpture of the Penrose Triangle (Perth, Australia), all sides of which are perpendicular to each other. 
And this is what the sculpture looks like from the other side. 
If you like impossible figures, you can admire them
An impossible figure is one of the types of optical illusions, a figure that at first glance seems to be a projection of an ordinary three-dimensional object,
upon closer examination of which contradictory connections of the elements of the figure become visible. An illusion is created of the impossibility of the existence of such a figure in three-dimensional space.
Impossible figures
The most famous impossible figures are the impossible triangle, the endless staircase and the impossible trident.
Impossible Perrose Triangle
The Reutersvard Illusion (Reutersvard, 1934)
Note also that the change in the figure-ground organization made it possible to perceive the centrally located "star".
_________
Escher's impossible cube
In fact, all impossible figures can exist in the real world. So, all objects drawn on paper are projections of three-dimensional objects, therefore, it is possible to create such a three-dimensional object that, when projected onto a plane, will look impossible. When looking at such an object from a certain point, it will also look impossible, but when viewed from any other point, the effect of impossibility will be lost.
The 13-meter aluminum sculpture of the impossible triangle was erected in 1999 in the city of Perth (Australia). Here the impossible triangle was depicted in its most general form - in the form of three beams connected to each other at right angles.
Devil's fork
Among all the impossible figures, the impossible trident ("devil's fork") occupies a special place. 
If you close the right side of the trident with your hand, then we will see a very real picture - three round teeth. If we close the lower part of the trident, then we will also see a real picture - two rectangular teeth. But, if we consider the whole figure as a whole, it turns out that three round teeth gradually turn into two rectangular ones.
Thus, you can see that the foreground and background of this drawing are in conflict. That is, what was originally in the foreground goes back, and the background (middle tooth) crawls forward. In addition to changing the foreground and background, this drawing has another effect - the flat edges of the right side of the trident become round in the left.
The effect of impossibility is achieved due to the fact that our brain analyzes the contour of the figure and tries to count the number of teeth. The brain compares the number of teeth of the figure in the left and right parts of the picture, which causes a feeling of the impossibility of the figure. If the figure had a significantly larger number of teeth (for example, 7 or 8), then this paradox would be less pronounced.
Some books claim that the impossible trident belongs to a class of impossible figures that cannot be recreated in the real world. Actually it is not. ALL impossible figures can be seen in the real world, but they will look impossible only from one single point of view.
______________
impossible elephant
How many legs does an elephant have?
Stanford psychologist Roger Shepard used the idea of a trident for his picture of the impossible elephant.
______________
Penrose stairs(endless staircase, impossible staircase)
The Infinite Stair is one of the most famous classical impossibilities.
It is a staircase design in which, in the case of movement along it in one direction (counterclockwise in the figure to the article), a person will rise indefinitely, and when moving in the opposite direction, he will constantly descend.
In other words, we see a staircase leading, it would seem, up or down, but at the same time, the person walking along it does not rise or fall. Having completed his visual route, he will be at the beginning of the path. If you really had to walk up that ladder, you would go up and down it aimlessly an infinite number of times. You can call it an endless Sisyphean labor!
Since the Penroses published this figure, it has appeared in print more often than any other impossible object. The "Endless Stair" can be found in books about games, puzzles, illusions, textbooks on psychology and other subjects.
"Ascent and Descent"
The "Endless Stairway" was successfully used by the artist Maurits K. Escher, this time in his charming 1960 Ascending and Descent lithograph.
In this drawing, which reflects all the possibilities of the Penrose figure, the quite recognizable Endless Staircase is neatly inscribed in the roof of the monastery. The hooded monks move continuously up the stairs in a clockwise and counter-clockwise direction. They go towards each other on an impossible path. They never manage to go up or down.
Accordingly, The Endless Stair became more often associated with Escher, who redrawn it, than with the Penroses, who conceived it.
How many shelves are there?
Where is the door open?
Out or in?
Impossible figures occasionally appeared on the canvases of the masters of the past, for example, such is the gallows in the painting by Pieter Brueghel (the Elder)
"Magpie on the gallows" (1568)
__________
Impossible arch
Jos de Mey is a Flemish artist who studied at the Royal Academy of Fine Arts in Ghent (Belgium) and then taught interior design and color to students for 39 years. Beginning in 1968, drawing became his focus. He is best known for his meticulous and realistic execution of impossible structures.
The most famous impossible figures in the works of the artist Maurice Escher. When considering such drawings, each individual detail seems quite plausible, however, when trying to trace the line, it turns out that this line is already, for example, not the outer corner of the wall, but the inner one.
"Relativity"
This lithograph by the Dutch artist Escher was first printed in 1953.
The lithograph depicts a paradoxical world in which the laws of reality do not apply. Three realities are united in one world, three forces of gravity are directed perpendicular to one another.
An architectural structure has been created, realities are connected by stairs. For people living in this world, but in different planes of reality, the same ladder will be directed either up or down.
"Waterfall"
This lithograph by the Dutch artist Escher was first printed in October 1961.
This work by Escher depicts a paradox - the falling water of a waterfall controls a wheel that directs water to the top of the waterfall. The waterfall has the structure of the "impossible" Penrose triangle: the lithograph was created based on an article in the British Journal of Psychology.
The design is made up of three crossbars laid on top of each other at right angles. The waterfall on the lithograph works like a perpetual motion machine. It also seems that both towers are the same; actually the one on the right, one floor below the left tower.
Well, more modern work: o)
Endless photography
Amazing construction
Chess board
upside down pictures
What do you see: a huge crow with prey or a fisherman in a boat, a fish and an island with trees?
Rasputin and Stalin
Youth and old age
_________________
Noble and Queen
___________________
Angry and Funny
The name itself is confusing: "impossible form." How can any form be impossible? If someone draws a given figure, then it exists. Indeed, they can be drawn, just not created in three dimensions.
Impossible figures is a type of optical illusion. When we look at a drawing in 2D, our brain automatically interprets the depicted element as a 3D object as it tries to understand the types and symbols. But in this case, they are drawn with spatial inconsistencies, creating a depth that is not - or cannot be - in real life. The subconscious mind struggles to process drawings that are “wrong”, trying to turn them into something real and understandable. But he can't.
Are you surprised? Let's look at some impossible shapes and how you can draw them. This will help you better understand what they are and how they work.
The most famous impossible shapes
Let's imagine four of all the most famous impossible figures:
- Penrose triangle (or also called tribar),
- penrose stairs,
- optical box
- impossible trident.
Penrose triangle 
Penrose stairs
All of them provide opportunities both for valuable exploration of human perceptual processes and for bringing joy and charm. Such works reveal the endless fascination of humanity with creativity and unusualness. These examples can also help us understand that our own perception may be limited or different from another person's perception of the same thing.
How to draw impossible figures?
Imagine the following. You wanted to try your hand at drawing to recreate an impossible shape. No wonder. Remember how fun it was as a kid when someone first showed you how to draw a cube? You'll draw one square, then another that was halfway on top of the first, and then connect them with diagonal lines. And here's a cube for you!
While there are many complex impossible shapes that would be difficult for most people, you can use one simple method to create one of the many common shapes: squares, triangles, stars, and pentagons. Let's draw a triangle.
- Draw a triangle.
- Extend the line from each corner.
- Draw a different line from each of these extensions that extend slightly into the corners.
- We're almost done! At the end of each line, draw a short 45 degree angle that aligns with the opposite side.
- Now for the fun part: Connect the lines and you'll have an impossible shape!
Use this basic set of instructions to create impossible shapes from other shapes. It should be pretty easy.
How impossible shapes inspire art
Impossible objects are fascinating. You can study them for long periods of time, tracing their lines, trying to figure out exactly where the "trick" is that they look real, and at the same time unreal. Not surprisingly, they often inspire artists to recreate them. Perhaps the most famous artist in the world of impossible constructions is M. C. Escher.
Maurits Escher- born in the Netherlands, an outstanding Dutch graphic artist, known throughout the world as a master of graphic illusions.
He produced about 450 lithographs, woodcuts and woodcuts during his lifetime, plus over 2,000 drawings and sketches. He was fascinated by impossible objects and helped popularize the Penrose Triangle, which he included in many of his works.
