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.
"Star Corona," by George W. Hart (www.georgehart.com)
This 8-inch, diameter, one-of-a-kind, acrylic sculpture consists of an inner red star surrounded by a yellow corona. It is designed to hang and the two components do not touch each other. The star has twelve large 5-sided spikes and twenty smaller 3-sided spikes, all assembled from sixty identical angular components. The corona is assembled from twenty identical curved components, which give the effect of swirling motion. If you look straight down on a spike, you see that arms from five of the yellow parts combine to make a circle around the spike. Both components are based on stellations of the icosahedron. The outer corona is based on the first stellation and the inner star shape is based on number 53 in the list by Coxeter et al. To understand it well, make a paper model from the instructions on my website.