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.
"Shells 532," by Chaim Goodman-Strauss, University of Arkansas (http://mathbun.com/main.php)
There are seven infinite families, and seven more individual types of discrete symmetrical patterns on the sphere. A pattern of type 532 is shown; there are three kinds of gyration points in the pattern--a 5-fold, a 3-fold, and a 2-fold gyration point are marked. This image is from "The Symmetries of Things", by John H. Conway, Heidi Burgiel and Chaim Goodman-Strauss (AK Peters, 2008).