Area 5. Three-dimensional and Mathematical Forms

The works featured in this section constitute an endeavour in pursuit of the visual reconstruction of three-dimensional objects and reveal his obsession with representing unstable and impossible worlds. Escher always held a curious interest in scientific advancements. His work is yet another example, alongside other artists of the time, of how artistic ingenuity can redirect scientific metaphors towards an individual and subjective source of inspiration.

Escher’s interest in crystallography is made evident in the works in this series. It was an interest he shared with his brother Berend George, a renowned geologist and professor at the University of Leiden. His interpretation of polyhedral figures inhabited by strange bodies increasingly drew him closer to conceptualising his work in a scientific manner.

By keenly confronting the enigmas that surround us, and by considering and analysing the observations that I have made, I ended up in the domain of mathematics. Although I am absolutely without training in the exact sciences, I often seem to have more in common with mathematicians than with my fellow artists.

This unconscious and natural move towards the world of science may be observed in the work Depth (1955), in which Escher plays with several of his favourite themes: the relativity of vanishing points, perspective and the infinite repetition of motifs. The work illustrates the existence of two worlds situated between the realms of the scientific and the surreal.

In fact, on creating unknown spaces with everyday objects and platonic bodies, the concept captured by Escher in his work is related to an attitude not far from the principles of Surrealism.


Escher’s work is that of an enthusiast, who through curiosity is drawn towards science, fascinated by its discoveries, trying to understand science from outside the field of study. His meticulous and precise work put him into contact with crystallography. He was very passionate about this specialty due to the countless possibilities it offered to create regular figures.

In his search to find forms to cover plane surfaces, in 1924 he came across the article “The analogy of the crystal symmetry in the plane” of the Hungarian mathematician George Pólya. The article describes the classification of the plane symmetry groups and explains, that the apparently endless ways to cover a plane surface with tiles in a parallelogram is reduced significantly to seventeen. Escher had just discovered the key to understand the decorative structures of the tiles in the Alhambra, which allowed him to develop his own rules to create symmetric planes and design his incredible etchings.


  • Three spheres I
    Three spheres I
  • Stars
  • Double planetoid
    Double planetoid
  • Contrast (order and chaos)
    Contrast (order and chaos)
  • Gravity
  • Spirales
  • Depth
  • Order and chaos
    Order and chaos
  • Rind
  • Bond of union
    Bond of union
  • Flatworms