Escher’s imagination took a simple geometric shape and turned it into a world.
A tetrahedron has a simple but elegant shape – like a pyramid built on a triangular base. The measurement along each edge is the same; each side is the same size; if you measure from the center of any side to the opposite tip, the measurements will be the same. It is pleasingly symmetrical.
Though the shape is simple, trying to reproduce the shape in two dimensions is not. You have to find the right cues to help the brain see the visible surfaces as if they were three dimensional, and to imagine the surfaces it cannot see.
Movement can help. With computers, we can represent it turning, so that we seem to see all sides and it looks more like a three dimensional shape.
Escher saw it differently. His imaginative understanding of the shape made it into something unexpected – he turned it into a world of its own, with buildings, people, plants and land. In his “Tetrahedral Planetoid” he chose to show two sides of the shape, with the line where they meet running down the middle. A tip found at ThinkQuest.org: it’s easier to see the shape within the image if you know that all the buildings point into the centre and that the ‘horizontal’ surfaces follow the shape of the outside sphere.
The illusion is so seductive that it is attempting to try to reproduce the two dimensional image as a three dimensional object, as Ziggy at PeripheralArbour.com did. You can see what he was able to recreate in the series of pictures he posted here.
From solid to illusion to object…
Image: M. C. Escher’s Tetrahedral Planetoid:
Image of turning tetrahedron from Wikimedia Commons, under Creative Commons Share Alike license, created by Peter Steinberg