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.
"15 Irregular Hexahedra," by Aaron Pfitzenmaier (student)
Honorable Mention, 2015 Mathematical Art Exhibition
This model was made from 180 units of four different types. It consists of 15 irregular hexahedra interlocked together. Each hexahedron has 2-fold dihedral symmetry and the positioning of each hexahedron is based on a pair of opposite edges on an icosahedron. This compound has the most complex weaving pattern out of anything I have designed, and is an example of a model where I extensively used the ray tracer POV-Ray as well as a computer program I wrote to aid in the design and folding/assembly process. --- Aaron Pfitzenmaier (http://bit.ly/aaronsorigami)