Escher working in three dimensions
M.C. Escher is recognized for his two-dimensional works, few people are aware of the sculptures he created. The top picture shows Escher holding up a lattice sculpture he created as a template for Cubic Space Division. The next pictures show Escher holding a tessellated rhombohedron. The tessellation was never a woodcut or lithograph, but it was one of his symmetry drawings.
A spherical tessellation is not a two-dimensional tessellation simply wrapped around sphere. A square will not tessellate around a sphere. A regular pentagon will tessellate around a sphere, but not on a plane. Please note that I said “regular” pentagon. Going into the mathematic details of which shapes tessellate and in which situation is beyond the scope of this website and beyond my abilities to explain reality (and if it really exists). This one of a kind Angels and Demons sphere proves Escher could carve more than wood blocks.
Does the starfish stellated dodecahedron remind you of an Escher lithograph? It should!
It is the same structure used in the lithograph Gravity.
Thank you to Bruno Ernst for his excellent book and for the photograph of Escher in his studio.