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.
"Morning Glories 4_2 : 2," by Chaim Goodman-Strauss, University of Arkansas (http://mathbun.com/main.php)
In addition to the thirty-five "prime", discrete symmetry types of three-dimensional Euclidean space, there are 184 "composite", types; these each can be projected down an axis to produce one of the 17 discrete symmetry types of the plane. This pattern in space, for example, with type 4_2 : 2, is a kind of attenuated planar pattern with type 4 * 2. This image is from "The Symmetries of Things", by John H. Conway, Heidi Burgiel and Chaim Goodman-Strauss (AK Peters, 2008).