# Conan Chadbourne

My work is motivated by a fascination with the occurrence of mathematical and scientific imagery in traditional art forms, and the frequently mystical or cosmological significance that can be attributed to such imagery. Mathematical themes both subtle and overt appear in a broad range of traditional art, from Medieval illuminated manuscripts to Buddhist mandalas, intricate tilings in Islamic architecture to restrained temple geometry paintings in Japan, complex patterns in African textiles to geometric ornament in archaic Greek ceramics. Often this imagery is deeply connected with how these cultures interpret and relate to the cosmos, in much the same way that modern scientific diagrams express a scientific worldview. I am especially interested in symmetry as a mechanism for finding order in the universe, from its intuitive appearance in ancient cosmological diagrams to its important role in modern theoretical physics, and my recent works explore various forms of symmetry.

This image is based on a presentation of the icosahedral group by generators of order 2 and 3, shown in red and green, respectively.

This work is part of a series of visual meditations on the structure of the alternating group on 5 elements, also known as the icosahedral group. This group is the smallest non-abelian simple group, and it characterizes the orientation-preserving symmetries of the regular icosahedron and dodecahedron. It also has interesting historical significance as one of the first groups to be studied abstractly, through its connection with the theory of quintic equations. This image explores the structure of the icosahedral group through a particular presentation by two generators. The group's elements, which appear as yellow disks in this image, are arranged at the vertices of a truncated icosahedron, shown here in stereographic projection, while the group's generators, of orders 2 and 5, correspond to the regions between the disks, colored red and blue, respectively. The image is composed of multiple hand-drawn images which are digitally composited and output as a archival digital print.