The connection between mathematics and art goes back thousands of years. Mathematics has been used in the design of Gothic cathedrals, Rose windows, oriental rugs, mosaics and tilings. Geometric forms were fundamental to the cubists and many abstract expressionists, and award-winning sculptors have used topology as the basis for their pieces. Dutch artist M.C. Escher represented infinity, Möbius bands, tessellations, deformations, reflections, Platonic solids, spirals, symmetry, and the hyperbolic plane in his works.
Mathematicians and artists continue to create stunning works in all media and to explore the visualization of mathematics--origami, computer-generated landscapes, tesselations, fractals, anamorphic art, and more.
This six-inch diameter paper sculpture is made of sixty identically shaped parts. Parts of any one color form a type of tetrahedron, and there are five such, deeply interlocked. No glue is used; they parts just hook into each other. I call this type of design "modular kirigami". It took me about four hours to assemble after several hours of false starts and figuring out how to do it. I generated a computer-rendered view down a five-fold axis. The "8"-shaped parts each link with many others. So they could not be made as single pieces of paper unless they were glued or taped together after being linked. But I wanted to be a purist and use no glue or tape, so I designed the parts as two overlapping "3"-shaped pieces.