Proceedings of Bridges 2025: Mathematics and the Arts
Pages 13–20
Invited Papers
Abstract
Duality is a concept in mathematics that underlies “Dubbel Planetoïde” (1949) and “Kristal” (1947), two prints by M.C. Escher. In these prints, we see a perfect combination of two polyhedra that apparently can hardly do without each other. In Escher’s print “Kristal,” both the cube and the octahedron are drawn as solid shapes. In this paper, I have now opted for an extra reversal: instead of both shapes being solid, I have replaced one of the two shapes with the skeleton of the shape. So, the cube is replaced with a figure that you get by extruding all the edges of the cube to the center of the cube; a figure consisting of twelve triangles. The result is that the combination has now become an easy to assemble construction.