Flatworms

In December 1958 and January 1959, Escher worked on a new print that he intended to display at an exhibition in Museum Boymans in February. Adopting the group name Vier Grafici (‘Four Graphic Artists’), he was exhibiting with Harry van Kruiningen, Wout van Heusden and Harry Disberg. A company he had been in before. He wrote about the print in a letter to his son George and his wife Corrie:*

“After a week of endless dispiration, I again find myself exploring tetrahedral and octahedral space: caves and caverns, wondrous pillars, abysses and vistas, all rigorously four-sided and eight-sided. My plan now is to finally have the cross-eyed flatworm I love swim in it.”

He continued in the next letter:**

“Tetrahedrons alternating with octahedrons, for example, can be placed against each other just as well as ordinary rectangular building blocks, in order to fill the space continuously. This print shows a building made of these two basic forms.”

The result is the lithograph Flatworms. An ingenious variation on Relativity and House of Stairs, which is populated not by humans but by one of the simplest life forms on earth: flatworms. A life form for which Escher had a soft spot, as he said himself. Perhaps because they are symmetrical: their left and right sides are mirror images of each other. He knew the creature from Animals without Backbones, a biology textbook that he had studied with great interest. The book deals with all manner of invertebrates, and Escher was fascinated by these strange life forms. It inspired him to produce several prints, including Plane Filling II, which features a large number of invertebrates. His memories of his time at the Municipal Grammar School in Arnhem may also have played a role. He had a Natural History teacher there, the zoologist Anthonie Cornelis Oudemans (1858-1943), who had obtained his doctorate in flatworms and undoubtedly talked about them in his lessons. Escher was not particularly interested in school, but he got on well with Oudemans (and with his art teacher F.W. van der Haagen). Writing about Oudemans, he said that he:***

“was greatly admired for his extensive knowledge and the generosity with which he communicates this.”

Oudemans wrote a book about sea snakes that went on to become famous (The Great Sea Serpent, 1882) and generated plenty of scepticism among his colleagues. It is not known whether Escher was familiar with this book.

Because flatworms generally live in water, Escher situates their home underwater. An illusion he achieves by (for example) introducing horizontal accentuation that illustrates the movement of the water. Just like the curl-ups in House of Stairs, the flatworms live in their own habitat. As if they were inhabitants of a peculiar aquarium.

Escher describes the structure like this:****

“Bricks are usually rectangular, because in that way they are most suitable for building the vertical walls of our houses. But anyone who has anything to do with the stacking of stones of a non-cubic type will be well aware of other possibilities. For instance, one can make use of tetrahedrons alternating with octahedrons. Such are the basic shapes which are used to raise the building illustrated here. They are not practicable for human beings to build with, because they make neither vertical walls nor horizontal floors. However, when this building is filled with water, flatworms can swim in it.”

Hence the flatworms’ habitat is composed entirely of tetrahedrons and octahedrons, interlinked four-sided pyramids. It takes some spatial imagination to envisage such a space, but Escher did not shy away from it. He was already familiar with these forms, three-dimensional models of which he had hanging in his studio.

Although the space in Flatworms has no vertical walls and no horizontal ceilings or floors, Escher points out in his correspondence with Bruno Ernst that:*****

“Despite the absence of horizontal and vertical planes, stacking tetrahedrons and octahedrons vertically allows one to build columns or pillars that, when viewed as a whole, stand vertically.”

The print shows five of these columns, of which the two on the right are two different variants. The rightmost one is a stack of octahedrons and the one next to it a stack of tetrahedrons. The play of symmetry and mirroring, the accurate perspectival depiction of the sloping walls and floors, and the way in which the tetrahedrons and octahedrons manifest themselves in this space is like a complicated puzzle. A puzzle that must have caused Escher a lot of headaches, but must also have given him a great deal of pleasure.

Structures based on triangles, tetrahedrons and octahedrons or with sloping walls and ceilings are rare but do occur. And they usually produce special results. Consider in this regard the work of Richard Buckminster Fuller (1895 – 1983), for instance. His geodesic domes, self-supporting structures consisting entirely of triangles, attract particular attention. He had not invented these himself, by the way, but he acquired the US patent on them and managed to publicise the domes. They were used for large buildings (the Montreal Biosphere built for Expo 67), though also for experimental houses and in a science-fiction film like Silent Running. The storage containers in it are built like truncated tetrahedrons. In science fiction, these geometric shapes symbolise technological progress. Biosphere 2 is an American research facility in Arizona that was once built to demonstrate the viability of closed ecological systems to enable human life in space. The buildings contain many triangles and geodesic domes. Think also of the famous cube houses in Helmond and Rotterdam, the walls and floors of which are straight, but the whole space is tilted.

Source
* Letter to George and Corrie, 21 December 1958. Wim Hazeu, M.C. Escher, Een biografie, Meulenhoff, 1998, page 405
** Letter to George and Corrie, 18 januari 1959. Wim Hazeu, M.C. Escher, Een biografie, Meulenhoff, 1998, page 405-406
*** Wim Hazeu, M.C. Escher, Een biografie, Meulenhoff, 1998, page 32
**** The 2013 reissue by Taschen GMBH of M.C. Escher. The Graphic Work. Originally published by Royal publishing house J.J. Tijl NV, Zwolle 1959, page 14
***** The Magic Mirror of M.C. Escher, Bruno Ernst, Taschen, 1976/2018, page 101